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Answer :
To find the average rate of change of the function
$$f(x)=1.6875x$$
between $x=3.9$ seconds and $x=8.2$ seconds, we follow these steps:
1. Calculate the value of the function at each time:
$$f(3.9)=1.6875(3.9)=6.58125,$$
$$f(8.2)=1.6875(8.2)=13.8375.$$
2. Find the change in the function values:
$$\Delta f=f(8.2)-f(3.9)=13.8375-6.58125=7.25625.$$
3. Determine the change in time:
$$\Delta t=8.2-3.9=4.3.$$
4. Compute the average rate of change using the formula:
$$\text{Average Rate of Change}=\frac{\Delta f}{\Delta t}=\frac{7.25625}{4.3}\approx1.69.$$
Thus, the average rate of change of the elevator’s speed between 3.9 seconds and 8.2 seconds is approximately
$$1.69\ \text{feet per second}.$$
$$f(x)=1.6875x$$
between $x=3.9$ seconds and $x=8.2$ seconds, we follow these steps:
1. Calculate the value of the function at each time:
$$f(3.9)=1.6875(3.9)=6.58125,$$
$$f(8.2)=1.6875(8.2)=13.8375.$$
2. Find the change in the function values:
$$\Delta f=f(8.2)-f(3.9)=13.8375-6.58125=7.25625.$$
3. Determine the change in time:
$$\Delta t=8.2-3.9=4.3.$$
4. Compute the average rate of change using the formula:
$$\text{Average Rate of Change}=\frac{\Delta f}{\Delta t}=\frac{7.25625}{4.3}\approx1.69.$$
Thus, the average rate of change of the elevator’s speed between 3.9 seconds and 8.2 seconds is approximately
$$1.69\ \text{feet per second}.$$
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