Question

Given an exponential function for compounding interest, A(x) = P(1.02)x, what is the rate of change?

Answer 1

A(x) = P(1.02)^x
A(x) = P(1 + 0.02)^x
A(x) = P(1 + r)^x

Therefore rate of change = 0.02 = 2%.

Answer 2

Answer:

The correct option is 1. The rate of change is 2%.

Step-by-step explanation:

The general growth function is

$A(x)=P(1+r)^x$ .... (1)

Where, P is initial value and r is rate of change.

The given exponential function for compounding interest is

$A(x)=P(1.02)^x$

The given function can be written as

$A(x)=P(1+0.02)^x$ ..... (2)

From (1) and (2) we get

$r=0.02$

In % it can be written as

$r=2\%$

Therefore the correct option is 1. The rate of change is 2%.