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Answer :
To find the average rate of change of the elevator's speed between 3.9 seconds and 8.2 seconds, we can follow these steps:
1. Understand the function: The speed of the elevator is given by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is the time in seconds.
2. Calculate the speed at the initial time: Plug in 3.9 seconds into the function:
[tex]\[
f(3.9) = 1.6875 \times 3.9
\][/tex]
3. Calculate the speed at the final time: Plug in 8.2 seconds into the function:
[tex]\[
f(8.2) = 1.6875 \times 8.2
\][/tex]
4. Find the change in speed: Subtract the speed at 3.9 seconds from the speed at 8.2 seconds:
[tex]\[
\Delta f = f(8.2) - f(3.9)
\][/tex]
5. Find the change in time: Subtract the initial time from the final time:
[tex]\[
\Delta x = 8.2 - 3.9
\][/tex]
6. Calculate the average rate of change: Divide the change in speed by the change in time:
[tex]\[
\text{Average rate of change} = \frac{\Delta f}{\Delta x}
\][/tex]
7. Round the result: Round the average rate of change to two decimal places.
Given the calculations, the average rate of change between 3.9 seconds and 8.2 seconds is approximately 1.69 feet per second.
So, the correct answer is: about 1.69 feet/second.
1. Understand the function: The speed of the elevator is given by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is the time in seconds.
2. Calculate the speed at the initial time: Plug in 3.9 seconds into the function:
[tex]\[
f(3.9) = 1.6875 \times 3.9
\][/tex]
3. Calculate the speed at the final time: Plug in 8.2 seconds into the function:
[tex]\[
f(8.2) = 1.6875 \times 8.2
\][/tex]
4. Find the change in speed: Subtract the speed at 3.9 seconds from the speed at 8.2 seconds:
[tex]\[
\Delta f = f(8.2) - f(3.9)
\][/tex]
5. Find the change in time: Subtract the initial time from the final time:
[tex]\[
\Delta x = 8.2 - 3.9
\][/tex]
6. Calculate the average rate of change: Divide the change in speed by the change in time:
[tex]\[
\text{Average rate of change} = \frac{\Delta f}{\Delta x}
\][/tex]
7. Round the result: Round the average rate of change to two decimal places.
Given the calculations, the average rate of change between 3.9 seconds and 8.2 seconds is approximately 1.69 feet per second.
So, the correct answer is: about 1.69 feet/second.
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