Applied-Algebra Exam Dumps - WGU Applied Algebra FXO2 PFXP C957

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:

â–­ ( " C " )

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 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 scatterplot shows the number of monthly train crossings decreasing over time. The decrease is not constant from one year to the next, so a linear model is not the best choice. Instead, the data decreases quickly at first and then begins to level off, which is characteristic of exponential decay. Exponential models are appropriate when a quantity changes by a repeated factor or percentage over equal time intervals. A logistic model would usually show an S-shaped pattern with a carrying capacity, and a polynomial model would be more appropriate for turning points or more complex curvature. Since the points show a smooth decreasing curve that flattens over time, an exponential function best models the data. Therefore, the correct answer is B.

The graph represents:

p(t)= " number of active players "

where:

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

We need to interpret the concavity between:

t=0.4

and

t=3.6

On this interval, the graph is rising, so the number of players is increasing.

But as the graph rises, it begins to level off near the top. This means the rate of increase is getting smaller.

So the number of players is not increasing faster and faster. Instead, it is increasing, but more slowly as time passes.

That means the graph is concave down on this interval.

The correct interpretation is:

" The number of players is increasing slower and slower. "

The function is:

f(x)=190× 〖 0.99 〗 ^x

Since xrepresents the number of years since 2003:

2012 ⇒ x=9

2015 ⇒ x=12

The average rate of change from 2012 to 2015 is:

(f(12)-f(9))/(12-9)

First, find f(9):

f(9)=190× 〖 0.99 〗 ^9

f(9)≈173.59

Now find f(12):

f(12)=190× 〖 0.99 〗 ^12

f(12)≈168.37

Now calculate the average rate of change:

(168.37-173.59)/(12-9)

=(-5.22)/3

≈-1.74

Rounded to the nearest whole number:

-2

The negative sign means the number of subscribers is decreasing.

So the correct interpretation is:

" The number of subscribers decreases at an average rate of about 2 subscribers per year. "

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 represents yearly profit as a function of time:

P(t)= " yearly profit "

where:

t= " years since opening "

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

From the graph, the highest point occurs at approximately:

t=10.5

So the maximum yearly profit happened approximately:

10.5 " years after opening "

The vertical axis measures yearly profit in millions of dollars. From the graph, the maximum value is approximately:

1.41

Since the units are millions of dollars:

1.41×1,000,000=1,410,000

So the maximum yearly profit was approximately:

$1,410,000

Therefore, the correct answer is:

â–­ ( " C " )