Question

Peter has saved $10. He doubles the amount he saves each week. Does this represent a exponential function? If so, please write down the function.

Answer 1

`y=10(2)^x`

Explanation:

This is an exponential function. Peter is not simply adding $10 a week to his savings, he's doubling each value each week. The first case of adding $10 a week is linear.

The standard form of an exponential equation is

`y=a(b)^x`

where a is the initial amount and b is the growth or decay factor. We know a = 10 because we are told he started with $10. After the first week he would have $20 then because $10 doubled is $20. That coordinate is (1, 20). We will use that in place of x and y and solve for b:

`20=10(b)^1`

b to the first is just b, so what we have essentially is 10b = 20, so b = 2. The equation then is:

`y=10(2)^x`