Problema Solution
the function y=1000(1.005)^x models that the value off $1000 depositat an interest in rate of 6% per year (.005 per month)x months after the deposited. How many months will it take for the account to reach %1100? Predict how many years it will take the money to be worth $1100?
Answer provided by our tutors
FIRST PART
(1+1100/100)*1000=12000=1000*(1.005)^x
If we cancel zeros, we have
12=1.005^x
Take both sides into log function,
ln12=x*ln(1.005)
then,
x=ln12/ln(1.005)=486.862~~487 months
SECOND PART
1100=1000*(1.005)^x
Then, we have
1.1=1.005^x and by using the same method above
x=ln(1.1)/ln(1.005)=19.11~~20 months(1 year and 8 months)