Question

average rate of change quick check
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)
about 0.50 feet/second
about 1.50 feet/second
about 0.74 feet/second
about 4.25 feet/second

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 3.9\), \(b=8.2\), and \(f(x)=1.6875x\).

Step2: Calculate \(f(a)\) and \(f(b)\)

• For \(x = a=3.9\), \(f(3.9)=1.6875\times3.9 = 6.58125\)
• For \(x = b = 8.2\), \(f(8.2)=1.6875\times8.2=13.8375\)

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(8.2)-f(3.9)}{8.2 - 3.9}=\frac{13.8375 - 6.58125}{4.3}\)
First, calculate the numerator: \(13.8375-6.58125 = 7.25625\)
Then, divide by the denominator: \(\frac{7.25625}{4.3}\approx1.69\)

Answer:

About \(1.69\) feet/second.