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 $A(t) = 3A_0$.

$A_0 \cdot 2^{t/16} = 3 A_0$

$2^{t/16} = 3$

$\log_2\left(2^{t/16}\right) = \log_2(3)$

$\dfrac t{16} \log_2(2) = \log_2(3)$

$\dfrac t{16} = \log_2(3)$

$t = 16 \log_2(3) = \log_2\left(3^{16}\right)$

or approximately 23.5954 years.