Question

A sum of money doubles in 16 years. When will it triple? (Full process please)

Answer 1

The amount of money
`A` after
`t` years, starting with
`A_0`, is given by

`A(t) = A_0 \cdot 2^(t/16)`

It takes 16 years to double, so

`A(16) = A_0\cdot2^(16/16) = 2A_0`

We want to solve for
`t` such that
`A(t) = 3A_0`.

`A_0 \cdot 2^(t/16) = 3 A_0`

`2^(t/16) = 3`

`\log_2\left(2^(t/16)\right) = \log_2(3)`

`\frac t{16} \log_2(2) = \log_2(3)`

`\frac t{16} = \log_2(3)`

`t = 16 \log_2(3) = \log_2\left(3^(16)\right)`

or approximately 23.5954 years.