Free WGU Applied Algebra Applied-Algebra Exam Questions

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

The horizontal axis represents:

The vertical axis represents:

The graph gives two labeled points:

and

The average rate of change is:

Substitute the values:

Rounded to the nearest tenth:

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

Therefore, the correct answer is:

The graph shows a linear relationship between:

and

The cost of each additional board is the rate of change, or slope, of the line.

From the graph, two labeled points are:

and

This means:

When 0 boards are ordered, the total cost is .

When 10 boards are ordered, the total cost is .

Now calculate the slope:

So each additional board costs:

Therefore, the correct answer is:

We are told that computer B completes 12 more tasks than computer A.

Let:

and

The phrase ''12 more than'' means add 12 to the original amount:

So, if computer A completes tasks, computer B completes:

tasks.

For example, if computer A completed 50 tasks, then computer B completed:

Therefore, the correct answer is:

The graph represents:

where:

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:

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

the curve is dropping more and more steeply.

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

The graph is a logistic growth curve.

A logistic growth curve has two main concavity regions:

and

From the graph, the function increases faster and faster until about:

After , 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:

So the correct answer is:

We are given the function:

This is a linear function because it has the form:

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

We need to find:

That means substitute into the function:

Now multiply:

Then add:

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

The value

indicates a strong fit because it is very close to . This means the regression model explains much of the variation in the traffic-frequency data.

However, we also need to check whether the prediction at

is a reasonable extrapolation.

From the scatterplot, the observed data values appear to extend to about:

The predicted value is slightly beyond the observed data range, but not extremely far beyond it.

Since is still within a reasonable extrapolation range, and the model has a strong value, the prediction is appropriate.

Therefore, the correct answer is:

This question asks which town's population is growing at a faster rate.

Since both population graphs are straight lines, we compare their slopes.

The slope of a line represents the rate of change:

From the graph:

Town A starts at about thousand people and increases at a rate of about thousand people per year.

Town B starts at about thousand people and increases at a rate of about thousand people per year.

Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.

Compare the rates:

So Town B is growing faster than Town A.

We are told that this year's number of property sales is 6 less than last year's number of property sales.

Let:

and

Since this year's sales are 6 less than last year's sales, the function rule is:

The question says that the number of properties sold last year was:

Substitute into the function:

So the notation that correctly represents the number of property sales this year is:

This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.

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:

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

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

So the observed data range is about:

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

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

The interval:

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

Also, does 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: