Question

Rate of change, anyone?

Given an exponential function for compounding interest, A(x) = P(1.01)x, what is the rate of change?

0.01%
1%
1.01%
10%

Answer 1

Answer: Second option is correct.

Explanation:

Since we have given that

`A(x)=P(1.01)^x`

As we know the exponential function for compounding interest.

`A(x)=P(1+r)^x`

Here, r is the rate of change .

So, on comparing both the equations we get that

`1+r=1.01\\\\r=1.01-1\\\\r=0.01* 100\%\\\\r=1\%`

Hence, Second option is correct.

Answer 2

For this case we have a function of the form:

`y = A * (b) ^ x`
Where,
A: initial amount
b: rate of change
x: independent variable.
We then have the following function:

`A (x) = P (1.01) ^ x`
The exchange rate is:

`(1.01 - 1) * 100 = 0.01 * 100 = 1%`
Answer:
the rate of change is:
1%