Question

write an exponential decay function to model the situation. compare the average rates of change over the given intervals. initial value: 52 decay factor: 0.7 1≤x≤4 and 5≤x≤8 the exponential decay function to model the situation is f(x)=\square.

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential decay function is $f(x) = a \cdot b^x$, where $a$ is the initial value and $b$ is the decay factor with $0 < b < 1$.

Step2: Substitute given values

We are given that the initial value $a = 52$ and the decay factor $b = 0.7$. Substituting these values into the formula, we get $f(x)=52\times(0.7)^x$.

Answer:

$f(x) = 52(0.7)^x$