does anyone know the answer?

Question

Write an exponential decay function to model the situation. Compare the average rates of change over the given intervals.

initial​ value: 45

decay​ factor: 0.9

1≤x≤5

and

6≤x≤8

Answer 1

The general form of an exponential function is:

f(x) = a·b^x

where a is the initial value and b is the decay factor. In your problem, a = 45 and b = 0.9. Plug those numbers into the general equation above to get the function that models the situation.

To get the average rate of change over an interval, compute the slope of the line that connects the endpoints of the interval (it's called the secant line). For an interval running from x₁ to x₂, the slope formula for a straight line is:

slope = (f(x₂)-f(x₁)) / (x₂-x₁)

where f(x₁) and f(x₂) are the values of your function at x₁ and x₂. So for the interval 1 ≤ x ≤ 5:

slope = average rate of change = (f(5)-f(1)) / (5-1) = ?