Pass the WGU Courses and Certificates Applied-Algebra Questions and answers with ExamsMirror

The graph shows the water volume decreasing over time.

The vertical axis represents:

" Water volume in gallons "

The horizontal axis represents:

" Time in minutes "

The graph is an exponential decay curve. It decreases quickly at first, then levels off.

From the graph, the curve approaches a horizontal value near:

y=1,000

This means the horizontal asymptote is approximately:

y=1,000

Since the graph approaches 1,000 gallons, it will not decrease to 500 gallons according to this model.

The water volume does not change by a constant rate because exponential functions do not have constant additive change. Also, the graph decreases fastest at the beginning, not later.

We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year.

Let:

t=number of people who auditioned last year

and

A(t)=number of people expected to audition this year

Since this year’s number is 4 times last year’s number, the function is:

A(t)=4t

The question says that 330 people auditioned last year, so:

t=330

Now substitute 330 into the function:

A(330)=4(330)

A(330)=1320

So, the correct function notation is:

A(330)=1,320

This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.

Therefore, the correct answer is:

B

The coefficient of determination, r

2

, measures how well a regression model fits the data. A value close to 1 indicates a strong fit, while a lower value indicates that the model does not explain the data as reliably. Here, r

2

=0.45, which is below 0.7. That means the model does not have a strong enough fit for reliable extrapolation in this question. Extrapolation means using the model to predict values outside the observed data range, which is riskier than interpolation. Because the model fit is not strong, choosing an extended range of x-values would not be appropriate. The correct reason is that extrapolation is not appropriate because r

2

< 0.7. Therefore, the answer is D.

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 us to interpret a value from a graph.

The horizontal axis represents:

Days

The vertical axis represents:

Practice duration in minutes

We need to find the practice duration on day 8.

To do this:

Locate 8 on the horizontal axis.

Move vertically until you reach the blue graph.

Read the corresponding value on the vertical axis.

From the graph, when:

x=8

the blue graph is at:

y=115

So the musician practiced for:

115 minutes

The graph represents:

p(t)= " number of active players "

where:

t= " hours after 11:00 a.m. "

The phrase “decreasing faster and faster” means two things are happening:

The graph is going downward, so the number of players is decreasing.

The graph is becoming steeper downward, so the rate of decrease is increasing.

This corresponds to a graph that is decreasing and concave down.

Looking at the graph, the number of active players reaches a maximum around:

t≈9

After that, the graph begins decreasing. Near the far right side of the graph, especially around:

t=11.2 " to " t=11.5

the curve is dropping more and more steeply.

That means the number of players is decreasing faster and faster on that interval.

We are given the function:

d(x)=14+65x

This is a linear function because it has the form:

d(x)=mx+b

where 65is the rate of change and 14is the starting value.

We need to find:

d(1.5)

That means substitute x=1.5into the function:

d(1.5)=14+65(1.5)

Now multiply:

65(1.5)=97.5

Then add:

d(1.5)=14+97.5

d(1.5)=111.5

So the distance from the tower to the object at 1.5seconds is:

111.5 " meters "

The scatterplot shows data collected over time, and a regression curve is used to model the pattern.

Extrapolation means using a model to make predictions slightly outside the observed data range. In Applied Algebra, extrapolation can be appropriate when:

" the regression model fits the data reasonably well "

and the predicted x-values are not too far outside the observed data.

From the scatterplot, the data points appear to run approximately from:

x=3 " to " x=15

So the observed data range is about:

15-3=12

A reasonable extrapolation range extends a little beyond the data, but not too far. The interval:

x=0 " to " x=18

extends about 3 units beyond each side of the observed data, which is reasonable.

The interval:

x=-3 " to " x=21

extends much farther beyond the data and would be less reliable.

Also, r^2does not have to equal exactly 1 for extrapolation to be useful. A value less than 1 can still represent a strong model.

Therefore, the correct answer is:

▭ ( " A " )

The graph represents the number of user accounts over time.

The horizontal axis represents:

" Time in months "

The vertical axis represents:

" Number of user accounts "

We need to find when the number of user accounts reached:

4,500

On the vertical axis, 4,500is halfway between:

3,000

and

6,000

So we look for the point where the blue curve reaches that height.

From the graph, the curve reaches approximately 4,500user accounts at:

x≈2.0

That means the website had about 4,500user accounts after approximately:

2.0 " months "

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 " )