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

Question

asked Jan 8, 2023 210k views

1 Answer

Dima Kornilov · Answer 1 · 2023-01-12T12:14:15+0000

The amount of money
after
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
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.