Question

Story problem! HELP! A parent increases a child's allowance by 15% each year. If the allowance is $3 now, how many years will it take to reach $15?
a) Write a equation and find the total amount of years

Answer 1

starting from 3,
next year, it will be A = 3+0.15*3=(1.15)*3
the year afterm A = (1.15)*(1.15)*3 = 3*(1.15)^2
after t years, A = 3*(1.15)^t
rearrange for t and solve
hint- log

Answer 2

Wait @electrokid do I solve for t at A = 3*(1.15)^t?

Answer 3

A= amount
t = time
thet want an equation for "t" in terms of A

Answer 4

So I solve for A. I am confused how to start this still... sorry :(

Answer 5

\[A/3=(1.15)^t\\
\ln({A\over3})=t\ln(1.15)\\
t=\frac{\ln(A)-\ln(3)}{\ln(1.15)}
\]

Answer 6

did you understand how I got A=3*(1.15)^t ?

Answer 7

now, the question gives you the amount $15. and asks how long will it take for that to happen!
so, we solve for "t" in the above equation.

Answer 8

Yes I understand how you got A=3**1.15)^t... Okay thank you :D