Free and Premium WGU Applied-Algebra Dumps Questions Answers

The function is:

f(x)=330× 〖 1.15 〗 ^x

Because xrepresents the number of years since 2005:

2006 ⇒ x=1

2011 ⇒ x=6

The average yearly rate of change from 2006 to 2011 is:

(f(6)-f(1))/(6-1)

First, find f(1):

f(1)=330× 〖 1.15 〗 ^1

f(1)=330×1.15

f(1)=379.50

Now find f(6):

f(6)=330× 〖 1.15 〗 ^6

f(6)≈330×2.31306

f(6)≈763.31

Now calculate the average rate of change:

(763.31-379.50)/(6-1)

=383.81/5

=76.762

Rounded to two decimal places:

76.76

So the average yearly rate of change of the artifact’s value from 2006 to 2011 is approximately:

$76.76 " per year "

Therefore, the correct answer is:

▭ ( " A " )

This situation can be modeled with a linear relationship because each box has the same weight.

We are given:

4 " boxes " →116 " pounds "

and

9 " boxes " →161 " pounds "

The weight increases because more boxes are added.

First, find the change in total weight:

161-116=45

Then find the change in the number of boxes:

9-4=5

Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:

45/5=9

So each box weighs:

9 " pounds "

Check:

If each box weighs 9 pounds, then adding 5 more boxes adds:

5(9)=45

116+45=161

This matches the given information.

The graph shows weekly profit as a function of time.

The horizontal axis represents:

" years since opening "

The vertical axis represents:

" weekly profit in hundreds of dollars "

The graph is an upward-opening curve, so its minimum value occurs at the lowest point, called the vertex.

From the graph, the lowest point occurs at approximately:

t=6

So the minimum weekly profit happened approximately:

6 " years after opening "

The vertical value at this point is approximately:

9.9

Since the profit is measured in hundreds of dollars:

9.9×100=990

So the minimum weekly profit was approximately:

$990

Therefore, the correct answer is:

▭ ( " A " )

The function is:

f(x)=1,300× 〖 0.92 〗 ^x

This is an exponential decay function because the base is between 0 and 1:

0 < 0.92 < 1

So the number of registered voters is decreasing over time.

Since xrepresents the number of years since 2001:

2001 ⇒ x=0

2007 ⇒ x=6

2008 ⇒ x=7

2009 ⇒ x=8

2012 ⇒ x=11

2021 ⇒ x=20

To determine the fastest average decrease, compare the average rates of change. A faster decrease means the average rate of change is more negative.

For 2001 to 2007:

(f(6)-f(0))/(6-0)

f(0)=1300

f(6)=1300(0.92)^6≈788.31

(788.31-1300)/6≈-85.28

So from 2001 to 2007, the number of registered voters decreased by about:

85.28 " voters per year "

For 2007 to 2008:

(f(7)-f(6))/(7-6)≈-63.06

For 2008 to 2021:

(f(20)-f(7))/(20-7)≈-42.58

For 2009 to 2012:

(f(11)-f(8))/(11-8)≈-45.13

Now compare the decreases:

-85.28, -63.06, -42.58, -45.13

The most negative rate is:

-85.28

That means the fastest average decrease happened from:

2001 " to " 2007

This is also a logistic growth curve.

Analyze the interval from month 2 to month 6:

The graph is increasing during this time.

The curve is becoming steeper, meaning the slope is increasing.

This indicates the rate of change is getting larger over time.

So, the number of affected acres is:

" increasing faster and faster "

This corresponds to the early-to-middle growth phase of a logistic function.

The average rate of change tells how much the output changes per one unit of input.

Here:

t= " hours after 5:00 a.m. "

and

n(t)= " number of animals "

The two given points are:

A=(1,10.6)

and

B=(8,6.59)

Use the average rate of change formula:

(y_2-y_1)/(x_2-x_1 )

Substitute the coordinates:

(6.59-10.6)/(8-1)

=(-4.01)/7

≈-0.573

The negative sign means the number of animals is decreasing.

So the correct interpretation is:

" The number of animals at the station decreases at an average rate of " 0.573 " animals per hour. "

Therefore, the correct answer is:

▭ ( " B " )

The graph compares the populations of two towns over time.

The horizontal axis represents:

" Time in years "

The vertical axis represents:

" Population in thousands "

The graph shows:

Town A as the solid blue line.

Town B as the dashed blue line.

To determine which town’s population is growing faster, we compare the slopes of the two lines.

In Applied Algebra, the slope of a line represents the rate of change:

" slope " = " change in population " / " change in time "

From the graph:

" Town A grows at about " 0.9 " thousand people per year "

" Town B grows at about " 1.6 " thousand people per year "

Now compare the growth rates:

1.6 > 0.9

So Town B’s population is growing at a faster rate.

The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.

This graph represents a logistic growth function, which has an S-shaped curve.

Key behavior of logistic functions:

Initial phase (early time) → growth is slow

Middle phase → growth speeds up (increasing rate)

Later phase → growth slows down as it approaches a maximum

Analyze the interval from day 1 to day 17:

This interval is in the early part of the graph.

The curve is increasing and getting steeper over this range.

That means the rate of increase is growing over time.

So, the number of comments is:

" increasing faster and faster "

The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.

The rate of change of a line is the slope:

" slope " =( " change in " y)/( " change in " r)

From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:

(2│9)

This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.

So the rate of change is:

9/2

That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.

The relationship can be written as:

y=9/2 r

So the correct interpretation is:

" The amount of yellow dye must be " 9/2 " of the amount of red dye. "

Therefore, the correct answer is:

▭ ( " A " )

The function M(t)represents the company’s market share after tyears.

The horizontal axis represents:

t= " time in years "

The vertical axis represents:

M(t)= " market share percentage "

We need to find when the market share reaches:

40%

From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.

The curve reaches 40%at approximately:

t=7.4

So the company should expect to have a market share of 40%after about:

7.4 " years "

Therefore, the correct answer is:

▭ ( " C " )

The regression model has:

r^2=0.99

This means the model is a very strong fit for the data because 0.99is close to 1.

However, a strong r^2value does not automatically make every prediction appropriate. We also have to check whether the x-value is within a reasonable extrapolation range.

The data shown on the graph appear to extend to about:

x=11

The prediction is for:

x=16.4

This is far beyond the observed data range. Even though the model fits the known data very well, predicting too far beyond the data can be unreliable.

The correct statement is that the r^2value indicates a strong fit, but x=16.4is more than 50%of the range beyond the maximum observed value.

Therefore, the correct answer is:

▭ ( " A " )

The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.

Here:

x= " hours after 7:00 a.m. "

and

y= " estimated wait time in minutes "

From the graph, point Ais approximately:

A=(5,88.3)

and point Bis approximately:

B=(9,65)

Now use the average rate of change formula:

" Average rate of change " =(y_2-y_1)/(x_2-x_1 )

Substitute the values:

(65-88.3)/(9-5)

=(-23.3)/4

=-5.825

Rounded to two decimal places:

-5.83

The negative sign means the estimated wait time is decreasing from point Ato point B.

So the average rate of change is approximately:

-5.83 " minutes per hour "

This question asks which town’s population is growing at a faster rate.

Since both population graphs are straight lines, we compare their slopes.

The slope of a line represents the rate of change:

" slope " = " change in population " / " change in time "

From the graph:

Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.

Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.

Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.

Compare the rates:

1.3 > 1.0

So Town B is growing faster than Town A.

The graph shows a decreasing exponential function.

The horizontal axis represents:

" Time in months "

The vertical axis represents:

" New user accounts per day "

The graph starts near 7,000new user accounts per day and decreases over time. However, it does not decrease toward 0. Instead, the graph levels off near a horizontal value around:

y=2,500

This horizontal value is the horizontal asymptote.

A horizontal asymptote shows the long-term value the function approaches. Since the asymptote is above 0, the model predicts that the number of daily new user accounts approaches a positive value, not zero.

So the justified statement is:

" The number of daily new user accounts will not decrease to 0. "

The function F(n) gives the number of animals in enclosure B.

The input n represents the number of animals in enclosure A.

The problem says enclosure B has 20 more animals than enclosure A. The phrase “20 more than” means we add 20:

F(n)=n+20

For example, if enclosure A had 30 animals, then enclosure B would have:

F(30)=30+20=50

So the function that represents the situation is:

F(n)=n+20

The function V(t)represents the number of travelers in the travel depot.

The input trepresents:

" hours after 7:00 a.m. "

The output V(t)represents:

" number of travelers "

So V(2)means the number of travelers in the depot:

2 " hours after 7:00 a.m. "

From the graph, when:

t=2

the value of V(t)is approximately:

79.2

Since V(t)measures travelers, not hours, V(2)represents:

79.2 " travelers "

Therefore, the correct answer is:

▭ ( " D " )

This question asks us to identify a correct conclusion from the graph.

The vertical axis represents:

" number of daily homework problems "

The horizontal axis represents:

" school days since the beginning of the term "

From the graph, the lowest point occurs at the far right, around:

" day " 22

The corresponding number of homework problems is approximately:

18

So the minimum number of daily homework problems is 18, and it occurs at day 22.

Therefore, the correct answer is:

▭ ( " D " )

The function is:

G(t)=1,600× 〖 1.31 〗 ^t

This is an exponential growth function because the base is greater than 1:

1.31 > 1

We need to find the population after 25 minutes, so substitute:

t=25

into the function:

G(25)=1,600× 〖 1.31 〗 ^25

Evaluate the exponent and multiply:

G(25)≈1,367,421.41

Since the population is a number of bacteria cells, round to the nearest whole number:

G(25)≈1,367,421

The graph shows a linear relationship between:

" Number of boards "

and

" Total cost "

The cost of each additional board is the rate of change, or slope, of the line.

From the graph, two labeled points are:

(0│27)

and

(10│177)

This means:

When 0 boards are ordered, the total cost is $27.

When 10 boards are ordered, the total cost is $177.

Now calculate the slope:

m=(177-27)/(10-0)

m=150/10

m=15

So each additional board costs:

$15

Therefore, the correct answer is:

▭ ( " B " )

The value r^2measures how well a regression model fits the data.

Here:

r^2=0.25

This is a low r^2value, meaning the model explains only about:

25%

of the variation in the data.

That indicates a weak fit. When a model has a weak fit, using it for extrapolation is not reliable because predictions outside the data range may be very inaccurate.

Since:

0.25 < 0.3

the best conclusion is that extrapolation is not appropriate because the regression model does not fit the data well enough.

Therefore, the correct answer is:

▭ ( " C " )

We are told that computer B completes 12 more tasks than computer A.

Let:

x= " number of tasks completed by computer A "

and

F(x)= " number of tasks completed by computer B "

The phrase “12 more than” means add 12 to the original amount:

F(x)=x+12

So, if computer A completes xtasks, computer B completes:

x+12

tasks.

For example, if computer A completed 50 tasks, then computer B completed:

F(50)=50+12=62

Therefore, the correct answer is:

▭ ( " B " )

This situation can be modeled using a linear relationship because each sack has the same weight.

We are given:

After 3sacks are removed, the total weight is 116pounds.

After 6sacks are removed, the total weight is 101pounds.

From 3 sacks removed to 6 sacks removed, the number of removed sacks increases by:

6-3=3

During that time, the total weight decreases from 116pounds to 101pounds:

116-101=15

So removing 3 additional sacks decreases the total weight by 15 pounds.

Now divide to find the weight of one sack:

15/3=5

So each sack weighs:

5 " pounds "

Check:

If 3 more sacks are removed and each sack weighs 5 pounds, the total weight should decrease by:

3(5)=15

116-15=101

This matches the given information.

We are told that this year’s number of property sales is 6 less than last year’s number of property sales.

Let:

x= " number of properties sold last year "

and

H(x)= " number of property sales this year "

Since this year’s sales are 6 less than last year’s sales, the function rule is:

H(x)=x-6

The question says that the number of properties sold last year was:

x=330

Substitute 330into the function:

H(330)=330-6

H(330)=324

So the notation that correctly represents the number of property sales this year is:

H(330)=324

This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.

The graph is a logistic growth curve.

A logistic growth curve has two main concavity regions:

" concave up before the inflection point "

and

" concave down after the inflection point "

From the graph, the function increases faster and faster until about:

x=6

After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.

This is concave down behavior.

Therefore, one interval where the graph is concave down is:

(6│11)

So the correct answer is:

▭ ( " D " )

From week 1 to week 7, the graph is increasing and becoming steeper.

In Applied Algebra, when a graph is increasing and its slope is getting larger, the quantity is said to be:

" increasing faster and faster "

This interval is on the early increasing part of the logistic curve, before the graph begins to level off.

Therefore, the correct answer is:

▭ ( " B " )

This question asks for the cost of each additional shirt, which means we need to find the rate of change of the linear function.

On a graph, the rate of change is the slope:

" slope " = " change in total cost " / " change in number of shirts "

From the graph, two labeled points are:

(0│33)

and

(10│173)

This means:

When 0shirts are ordered, the cost is $33.

When 10shirts are ordered, the cost is $173.

Now find the slope:

m=(173-33)/(10-0)

m=140/10

m=14

So the cost increases by:

$14

for each additional shirt.

The $33represents a fixed starting cost, not the cost per shirt.

The graph shows customer visits by day.

To determine which days likely featured new releases, we should look for the days with unusually high customer counts.

From the graph:

Day 8 has about 40customers.

Day 11 also has about 40customers.

These are the highest values shown on the graph.

Since the problem says more customers show up on days when new releases are featured, the days with the highest customer counts are the most likely new-release days.

Therefore, the correct answer is:

▭ ( " D " )

We are told that supervisor B has 13 more employees than supervisor A.

Let:

n= " number of employees under supervisor A "

and

F(n)= " number of employees under supervisor B "

The phrase “13 more than” means we add 13:

F(n)=n+13

So, if supervisor A has nemployees, supervisor B has 13 additional employees.

For example, if supervisor A had 20 employees, then supervisor B would have:

F(20)=20+13=33

Therefore, the correct answer is:

▭ ( " C " )