WGU Updated Applied-Algebra Exam Questions and Answers by kareem

To describe “decreasing slower and slower,” the graph must be moving downward while becoming less steep. This means the function values are decreasing, but the rate of decrease is becoming smaller in magnitude. On the graph of x(t), the number of users first increases, then decreases after reaching a local maximum. The interval from t=6.8 to t=7.4 lies on a decreasing part of the curve where the graph is beginning to flatten compared with the steeper earlier decrease. That behavior means the number of users is still going down, but not as quickly as before. The other intervals either occur while the graph is increasing or include behavior that does not consistently match decreasing slower and slower. Therefore, the correct answer is C.

The average rate of change measures how much the output changes per one unit of input. Here, the input is time in hours after 6:00 a.m., and the output is the number of vehicles stopped at the toll booth. The two given points are A=(1,49.4) and B=(4,45.8). Use the average rate of change formula: (y

2

​

−y

1

​

)/(x

2

​

−x

1

​

). Substituting the coordinates gives (45.8−49.4)/(4−1). The numerator is −3.6, and the denominator is 3, so the average rate of change is −1.2. The negative sign means the number of vehicles decreased over the interval.

The r

2

value of 0.41 indicates a moderate fit, not a strong fit. A moderate regression model may sometimes support limited extrapolation, but only if the prediction stays close to the observed data. Here, the prediction is made at x=19.4, which is beyond the maximum x-value shown in the scatterplot. For a moderate fit, extrapolation should be more conservative than for a strong fit. The value x=19.4 is more than 25% of the data range beyond the maximum observed value, so the prediction is too far outside the data. Because the fit is only moderate and the extrapolation distance is too large, the prediction is not appropriate. Therefore, the answer is B.

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.