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

Answer:

$y=10(2)^x$

Step-by-step 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:

$y=10(2)^x$