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

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

Because the vehicle is traveling away from the town at a fixed rate, the distance can be modeled by a linear function:

d(t)=mt+b

where:

m= " rate of change "

and

b= " initial distance from the town "

We are given two points:

(1│200)

and

(4│395)

These mean:

After 1hour, the vehicle is 200miles away.

After 4hours, the vehicle is 395miles away.

First, find the rate of change:

m=(395-200)/(4-1)

m=195/3

m=65

So the vehicle is moving away from the town at a rate of:

65 " miles per hour "

Now the function has the form:

d(t)=65t+b

Use the point (1│200)to find b:

200=65(1)+b

200=65+b

b=135

Therefore, the function is:

d(t)=65t+135

Check using t=4:

d(4)=65(4)+135

d(4)=260+135

d(4)=395

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 an increasing exponential curve.

The number of subscribers is going up as time passes, so the function is increasing.

Also, the graph becomes steeper as time increases. This means the rate of increase is getting larger.

So the number of subscribers is:

" increasing faster and faster "

This is a key feature of exponential growth.

The graph shows population in thousands, and the horizontal axis represents:

" years since 1995 "

Point Pis located at approximately:

x=12

Since xrepresents years since 1995:

1995+12=2007

So point Pcorresponds to the year:

2007

The instantaneous rate of change at point Pis:

3.74

Because the vertical axis is measured in thousands, this means:

3.74 " thousand animals per year "

Convert thousands to actual animals:

3.74×1000=3740

So in 2007, the population was increasing by approximately:

3,740 " animals per year "

Since xrepresents the number of years since 2004:

2013-2004=9

so:

2013 ⇒ x=9

Also:

2018-2004=14

so:

2018 ⇒ x=14

The average yearly rate of change from 2013 to 2018 is:

(f(14)-f(9))/(14-9)

Now evaluate the function:

f(9)=330× 〖 1.04 〗 ^9

f(9)≈469.37

f(14)=330× 〖 1.04 〗 ^14

f(14)≈571.13

Now calculate the average rate of change:

(571.13-469.37)/5

=101.76/5

=20.35

So the painting’s value increased by an average of about:

$20.35 " per year "

Therefore, the correct answer is:

▭ ( " A " )

The graph compares the spread of two viruses over time.

The horizontal axis represents:

t= " time in months "

The vertical axis represents:

" percentage of the population affected "

The graph shows:

Virus A as the solid blue curve.

Virus B as the dashed blue curve.

To determine which statement is correct, we compare when each virus reaches the same population percentage.

At 20%:

Virus B reaches 20%earlier, around t≈5months.

Virus A reaches 20%later, around t≈6.5months.

So Virus B affects 20%of the population before Virus A does.

For higher percentages such as 60%, 70%, and 80%, Virus A rises more quickly after about 50%, so Virus A reaches those percentages before Virus B.

Therefore, the correct conclusion is:

" Virus B affects " 20% " of the population before virus A does. "

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 " )