Answer:
[tex]y=10(2)^x[/tex]
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
[tex]y=a(b)^x[/tex]
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:
[tex]20=10(b)^1[/tex]
b to the first is just b, so what we have essentially is 10b = 20, so b = 2. The equation then is:
[tex]y=10(2)^x[/tex]
