Question

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

2%
0.02%
1.02%
102%
Would it be c?

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

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%.