Question
The table shows the amount of money, y, that Kareem earns in x hours.
Use the table to answer the question.
Hours (x) 0 2.5 6 8.75 10.25
Money (y) 0 48.45 116.28 169.58 198.65
What is the rate of change for the interval 2.5–8.75? Round your answer to the nearest cent.(1 point)
$
per hour
Which type of function is shown in the table? Enter your answer below from the list.
linear
quadratic
exponential
Use the table to answer the question.
Hours (x) 0 2.5 6 8.75 10.25
Money (y) 0 48.45 116.28 169.58 198.65
What is the rate of change for the interval 2.5–8.75? Round your answer to the nearest cent.(1 point)
$
per hour
Which type of function is shown in the table? Enter your answer below from the list.
linear
quadratic
exponential
Answers
GPT-4o mini
To find the rate of change for the interval from 2.5 to 8.75, we use the formula for the rate of change:
\[
\text{Rate of Change} = \frac{\text{Change in Money (y)}}{\text{Change in Hours (x)}}
\]
First, we need to determine the changes in y and x for the interval 2.5 to 8.75.
From the table:
- At \( x = 2.5 \), \( y = 48.45 \)
- At \( x = 8.75 \), \( y = 169.58 \)
Now, calculate the change in y and the change in x:
\[
\text{Change in } y = 169.58 - 48.45 = 121.13
\]
\[
\text{Change in } x = 8.75 - 2.5 = 6.25
\]
Now, plug these values into the rate of change formula:
\[
\text{Rate of Change} = \frac{121.13}{6.25} \approx 19.38
\]
Rounding to the nearest cent gives:
\[
19.38 \text{ dollars per hour}
\]
Now to identify the type of function that is shown in the table, we can observe the values of y as x changes. The increments in y do not appear to be consistent (indicating a non-linear relationship). Since the rate of change isn't constant (as shown by the varying increments in y for equal increments in x), the function is not linear.
The quickest way to determine the function type between quadratic and exponential would be to check how y increases as x increases. Given that the rate of change is increasing, this indicates a likely exponential function.
Thus, the type of function is:
**exponential.**
To summarize:
- Rate of change for the interval 2.5–8.75: **$19.38 per hour**
- Type of function: **exponential**
\[
\text{Rate of Change} = \frac{\text{Change in Money (y)}}{\text{Change in Hours (x)}}
\]
First, we need to determine the changes in y and x for the interval 2.5 to 8.75.
From the table:
- At \( x = 2.5 \), \( y = 48.45 \)
- At \( x = 8.75 \), \( y = 169.58 \)
Now, calculate the change in y and the change in x:
\[
\text{Change in } y = 169.58 - 48.45 = 121.13
\]
\[
\text{Change in } x = 8.75 - 2.5 = 6.25
\]
Now, plug these values into the rate of change formula:
\[
\text{Rate of Change} = \frac{121.13}{6.25} \approx 19.38
\]
Rounding to the nearest cent gives:
\[
19.38 \text{ dollars per hour}
\]
Now to identify the type of function that is shown in the table, we can observe the values of y as x changes. The increments in y do not appear to be consistent (indicating a non-linear relationship). Since the rate of change isn't constant (as shown by the varying increments in y for equal increments in x), the function is not linear.
The quickest way to determine the function type between quadratic and exponential would be to check how y increases as x increases. Given that the rate of change is increasing, this indicates a likely exponential function.
Thus, the type of function is:
**exponential.**
To summarize:
- Rate of change for the interval 2.5–8.75: **$19.38 per hour**
- Type of function: **exponential**