Question

the graph shows the population of a town that doubles every year and started with 100 people at year 0. After how many years will the population be at 600?

Answer 1

Answer:

2.6 years

Explanations:

At year 0, the population of the town = 100

Let a₀ represents the population at year 0

a₀ = 100

The population doubles every year, this means that the common ratio is 2.

Let the common ratio be represented as r

r = 2

The population after n years = 600

$\begin{gathered} \text{Let the population after n years be a}_n \\ a_n=\text{ 600} \end{gathered}$

Using the formula:

$\begin{gathered} a_n=a_0r^n^{} \\ 600\text{ = 100}\times2^n \\ \frac{600}{100}=2^n \\ 6=2^n \\ \text{Take the ln of both sides} \\ \ln 6=ln2^n \\ \ln 6=n\ln 2 \\ n\text{ = }\frac{\ln 6}{\ln 2} \\ n\text{ = }\frac{1.79}{0.69} \\ n\text{ = 2.59} \\ n\text{ = 2.6} \end{gathered}$