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 1.69 feet/second
about 1.69 feet/second

about 4.00 feet/second
about 4.00 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 function \( f(x) = 1.6875x \) between \( x = 3.9 \) seconds and \( x = 8.2 \) seconds, we use the formula for the average rate of change:

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

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

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

\[
f(3.9) = 1.6875 \times 3.9 = 6.57875 \text{ feet/second}
\]

\[
f(8.2) = 1.6875 \times 8.2 = 13.8375 \text{ feet/second}
\]

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

\[
\text{Average rate of change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9} = \frac{13.8375 - 6.57875}{8.2 - 3.9}
\]

Calculating the difference in speed:

\[
13.8375 - 6.57875 = 7.25875
\]

Calculating the difference in time:

\[
8.2 - 3.9 = 4.3
\]

Now calculate the average rate of change:

\[
\text{Average rate of change} = \frac{7.25875}{4.3} \approx 1.69 \text{ feet/second}
\]

After rounding to two decimal places, the average rate of change is:

\[
\text{Average rate of change} \approx 1.69 \text{ feet/second}
\]

Therefore, the correct response is:

**about 1.69 feet/second**