Answer :
To find the average rate of change of the elevator's speed between 3.9 seconds and 8.2 seconds, follow these steps:
1. Understand the Function: The speed of the elevator is modeled by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is time in seconds.
2. Calculate the Function Values:
- Find the value of the function at [tex]\( x = 8.2 \)[/tex]:
[tex]\[
f(8.2) = 1.6875 \times 8.2
\][/tex]
- Find the value of the function at [tex]\( x = 3.9 \)[/tex]:
[tex]\[
f(3.9) = 1.6875 \times 3.9
\][/tex]
3. Calculate the Difference:
- Compute the change in the function values:
[tex]\[
f(8.2) - f(3.9)
\][/tex]
4. Find the Average Rate of Change:
- Use the average rate of change formula:
[tex]\[
\text{Average Rate of Change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9}
\][/tex]
5. Round the Answer: Finally, round the result to two decimal places to get the average rate of change.
Following these computations, the estimated average rate of change between 3.9 seconds and 8.2 seconds is about 1.69 feet/second.
1. Understand the Function: The speed of the elevator is modeled by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is time in seconds.
2. Calculate the Function Values:
- Find the value of the function at [tex]\( x = 8.2 \)[/tex]:
[tex]\[
f(8.2) = 1.6875 \times 8.2
\][/tex]
- Find the value of the function at [tex]\( x = 3.9 \)[/tex]:
[tex]\[
f(3.9) = 1.6875 \times 3.9
\][/tex]
3. Calculate the Difference:
- Compute the change in the function values:
[tex]\[
f(8.2) - f(3.9)
\][/tex]
4. Find the Average Rate of Change:
- Use the average rate of change formula:
[tex]\[
\text{Average Rate of Change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9}
\][/tex]
5. Round the Answer: Finally, round the result to two decimal places to get the average rate of change.
Following these computations, the estimated average rate of change between 3.9 seconds and 8.2 seconds is about 1.69 feet/second.
