Question

The value of an investment A
(in dollars) after t years is given by the function A(t) = A0ekt
. If it takes 10 years for an investment of $1,000 to triple, how many years will it take for the investment to be $9,000? Simplify your answer completely.


I am very confused. So please show all work thank you

Answer 1

3 = 1 e^(10k)
10k = ln 3
k = ln3/10

so amount = 1000 e^( (ln3/10)t)
9000 =1000 e^( (ln3/10)t)
9 = e^( (ln3/10)t)
ln 9 = (ln3/10)t
ln9/(ln3/10)= t
t = 10ln9/ln3 = 20 years