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The function in the table below shows the relationship between the total number of houses built in an area and the number of months that passed.

\begin{tabular}{|c|c|}
\hline Months Passed & Total Houses Built \\
\hline 0 & 0 \\
\hline 3 & 33 \\
\hline 4 & 46 \\
\hline 8 & 108 \\
\hline
\end{tabular}

Which best describes the data set?

A. It is nonlinear because the "Total Houses Built" column does not increase at a constant additive rate.
B. It is nonlinear because the "Months Passed" column does not increase at a constant additive rate.
C. It is nonlinear because the increase in the "Total Houses Built" compared to the increase in the "Months Passed" does not show a constant rate of change.
D. It is linear because the increase in the "Total Houses Built" compared to the increase in the "Months Passed" shows a constant rate of change.

Sagot :

GinnyAnsweridn
To determine whether the given dataset represents a linear or nonlinear relationship, we need to check if the rate of change (or slope) between the data points is constant. This is done by comparing the differences in 'Total Houses Built' relative to the differences in 'Months Passed' across each interval.

The data points provided are:
- (0 months, 0 houses)
- (3 months, 33 houses)
- (4 months, 46 houses)
- (8 months, 108 houses)

Let’s calculate the rate of change for each of the intervals between these data points.

1. From 0 to 3 months:
- Houses built: 33 - 0 = 33
- Months passed: 3 - 0 = 3
- Rate of change: 33 / 3 = 11 houses per month

2. From 3 to 4 months:
- Houses built: 46 - 33 = 13
- Months passed: 4 - 3 = 1
- Rate of change: 13 / 1 = 13 houses per month

3. From 4 to 8 months:
- Houses built: 108 - 46 = 62
- Months passed: 8 - 4 = 4
- Rate of change: 62 / 4 = 15.5 houses per month

Now, let’s examine the calculated rates of changes:
- From 0 to 3 months: 11 houses per month
- From 3 to 4 months: 13 houses per month
- From 4 to 8 months: 15.5 houses per month

We observe that the rate of change is not constant; it varies from one interval to another.

Therefore, we conclude:

The relationship is nonlinear because the increase in the "Total Houses Built" compared to the increase in the "Months Passed" does not show a constant rate of change.
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