Given an exponential function for compounding interest, a(x) = p(.77)^x, what is the rate of change?

Solution:

Given, an exponential function for compound interest is a(x) = p(.77)^x

We have to find the rate of change.

The general form of an exponential function is

f(x) = a(1 + r)^x

Where, a is the initial amount

(1 + r) is the rate of change

r is the growth or decay factor.

Here, 1 + r = 0.77

r = 0.77 - 1

r = -0.23

Converting to percent,

r = -0.23 × 100

r = -23%

Therefore, the rate of change is -23%.

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Given an exponential function for compounding interest, a(x) = p(.77)^x, what is the rate of change?

Summary:

An exponential function for compounding interest, a(x) = p(.77)^x, the rate of change is -23%.