Find the base, b, for the exponential equation of the form y=a x b^x that describes each situation.

Question

A savings account earns 2% annual interest, compounded annually. The variable y gives the amount of money in the account after x years. Find the base, b, for the exponential equation of the form y=a x b^x that describes the situation.

Answer 1

Is your form supposed to be:

y=a(b^x) ??

 

Basic compound interest for interest compounded annually is:

A = P(1+r)^t

A = final or future amount...

      You are calling this "y"

P = principal/initial investment

      You are calling this "a"

r = interest rate as a decimal = .02

t = time in years

      You are calling this "x"

 

Your equation is then:

y = a(1+r)^x

 

y = a(1+.02)^x

 

y = a(1.02)^x

 

b = 1.02 within the bounds of your problem