Question

The speed of an elevator (in feet per second) is modeled by the function f(x)=1.6875x
, where x is time in seconds. Estimate the average rate of change between 3.9 seconds and 8.2 seconds. Round the final answer to two decimal places.(1 point)
Responses

about 4.00 feet/second
about 4.00 feet/second

about 1.69 feet/second
about 1.69 feet/second

about 6.75 feet/second
about 6.75 feet/second

about 0.59 feet/second

Answer 1

To estimate the average rate of change of the speed of the elevator between 3.9 seconds and 8.2 seconds, we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = 3.9 \) seconds and \( b = 8.2 \) seconds.

First, we need to calculate \( f(3.9) \) and \( f(8.2) \):

1. Calculate \( f(3.9) \):
\[
f(3.9) = 1.6875 \times 3.9 \approx 6.58575
\]

2. Calculate \( f(8.2) \):
\[
f(8.2) = 1.6875 \times 8.2 \approx 13.8375
\]

Now, we can substitute these values into the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9}
\]
\[
= \frac{13.8375 - 6.58575}{8.2 - 3.9}
\]
\[
= \frac{7.25175}{4.3}
\]
\[
\approx 1.68 \text{ feet/second} \quad (\text{to two decimal places})
\]

Therefore, the average rate of change between 3.9 seconds and 8.2 seconds is about **1.69 feet/second**.