WGU Applied-Algebra - WGU Applied Algebra FXO2 PFXP C957

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

The graph models the number of widgets the team can produce each day.

The horizontal axis represents:

" days "

The vertical axis represents:

" widgets "

The graph gives two labeled points:

(6│3.4)

and

(14│23)

The average rate of change is:

" change in widgets " / " change in days "

Substitute the values:

(23-3.4)/(14-6)

=19.6/8

=2.45

Rounded to the nearest tenth:

2.5

This means the team increased production by an average of approximately:

2.5 " widgets each day "

Therefore, the correct answer is:

â–­ ( " B " )

The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:

C(t)=mt+b

where:

m= " hourly rate "

and

b= " flat rate "

We are given two points:

(3│220)

and

(5│340)

These mean:

A 3-hour job costs $220.

A 5-hour job costs $340.

First, find the hourly rate using slope:

m=(340-220)/(5-3)

m=120/2

m=60

So the contractor charges:

$60 " per hour "

Now the function has the form:

C(t)=60t+b

Use the point (3│220)to find the flat rate:

220=60(3)+b

220=180+b

b=40

So the function is:

C(t)=60t+40

Check with t=5:

C(5)=60(5)+40

C(5)=300+40

C(5)=340

This matches the given information.

The graph represents:

p(t)= " number of people at the gym "

where:

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

The question asks about the concavity of the graph between:

t=1.3

and

t=3.4

On this interval, the graph is still going upward, so the number of people is increasing.

However, the graph is beginning to flatten as it approaches its highest point. That means the slope is positive, but the slope is getting smaller.

In other words:

" The number of people is increasing, but at a slower rate. "

This is called concave down behavior. For a concave down graph that is increasing, the correct interpretation is:

" increasing slower and slower "

Therefore, the correct answer is:

â–­ ( " C " )

The graph compares the spread of two viruses over time.

The horizontal axis represents:

" time in months "

The vertical axis represents:

" percent 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, compare when each virus reaches the same population percentage.

At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.

However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.

So the correct conclusion is:

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

Therefore, the correct answer is:

â–­ ( " A " )

The graph shows a decreasing exponential model.

The vertical axis represents:

" Licensed sellers "

The horizontal axis represents:

" Time in years "

The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:

y=100

That horizontal line is the horizontal asymptote.

A horizontal asymptote represents the long-term value the function approaches as time continues.

So the correct interpretation is:

" In the long run, the number of licensed sellers nears 100. "

Therefore, the correct answer is:

â–­ ( " C " )

The graph shows the temperature of an object decreasing over time.

The horizontal axis represents:

" Time in minutes "

The vertical axis represents:

" Temperature in degrees Fahrenheit "

The curve decreases and approaches the horizontal axis as time increases.

A horizontal asymptote is a horizontal line that the graph approaches but may not reach. Horizontal lines have equations of the form:

y= " constant "

From the graph, the curve approaches:

y=0

So the horizontal asymptote is:

y=0

The options x=0and x=500are vertical lines, not horizontal asymptotes.

Therefore, the correct answer is:

â–­ ( " B " )

This question asks for the break-even point, which is the point where:

Revenue=Cost

On the graph:

The solid blue line represents revenue.

The dashed blue line represents cost.

The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.

Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.

The graph shows the intersection occurs between:

4 and 5

So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.

Therefore, the correct answer is:

C

The function f(n) gives the distance traveled by vehicle B.

The input n represents the distance traveled by vehicle A.

The problem says vehicle B travels 17 more than vehicle A. The phrase “17 more than” means we add 17 to the amount traveled by vehicle A.

So the relationship is:

f(n)=n+17

For example, if vehicle A traveled 50 miles, then vehicle B traveled:

f(50)=50+17=67

So the correct function is:

f(n)=n+17

Therefore, the correct answer is:

B

The graph shows P(t), where:

t= " years since opening "

and

P(t)= " daily profit in hundreds of dollars "

The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.

From the graph, the highest point occurs at approximately:

t=9

So the maximum daily profit happened approximately:

9 " years after opening "

The vertical value at this maximum point is approximately:

P(t)=29

But the graph measures profit in hundreds of dollars, so:

29×100=2900

Therefore, the maximum daily profit was approximately:

$2,900

So the correct interpretation is:

" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "