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Answer :
To estimate the average rate of change of the function [tex]\( f(x) = 1.6875x \)[/tex] between 3.9 seconds and 8.2 seconds, follow these steps:
1. Calculate the value of the function at [tex]\( x = 3.9 \)[/tex]:
[tex]\[
f(3.9) = 1.6875 \times 3.9 = 6.58
\][/tex]
2. Calculate the value of the function at [tex]\( x = 8.2 \)[/tex]:
[tex]\[
f(8.2) = 1.6875 \times 8.2 = 13.84
\][/tex]
3. Find the difference in function values:
[tex]\[
f(8.2) - f(3.9) = 13.84 - 6.58 = 7.26
\][/tex]
4. Calculate the change in time:
[tex]\[
8.2 - 3.9 = 4.3
\][/tex]
5. Calculate the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{7.26}{4.3} \approx 1.69
\][/tex]
This rate of change tells us how much the speed of the elevator is changing, on average, per second over this interval. Therefore, the average rate of change is approximately 1.69 feet per second.
The correct answer is about 1.69 feet/second.
1. Calculate the value of the function at [tex]\( x = 3.9 \)[/tex]:
[tex]\[
f(3.9) = 1.6875 \times 3.9 = 6.58
\][/tex]
2. Calculate the value of the function at [tex]\( x = 8.2 \)[/tex]:
[tex]\[
f(8.2) = 1.6875 \times 8.2 = 13.84
\][/tex]
3. Find the difference in function values:
[tex]\[
f(8.2) - f(3.9) = 13.84 - 6.58 = 7.26
\][/tex]
4. Calculate the change in time:
[tex]\[
8.2 - 3.9 = 4.3
\][/tex]
5. Calculate the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{7.26}{4.3} \approx 1.69
\][/tex]
This rate of change tells us how much the speed of the elevator is changing, on average, per second over this interval. Therefore, the average rate of change is approximately 1.69 feet per second.
The correct answer is about 1.69 feet/second.
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