Question

A town has a population of 19000 and grows at 4% every year. To the nearest year, how long will it be until the population will reach 43500?

Answer 1

Answer:

1 year

Step-by-step explanation:

The population can be modelled by the equation:

$P=P_0(1 + r)^{t}$

From the question, the initial population is

$P_0=19000$

The annual growth rate is r=0.04

We want to find how long it will take for that population to reach 43500.

We substitute the values to get:

$43500=19000(1 + 0.04)^{t}$

$435=190(1.04)^{t}$

$\frac{435}{190} = (1.04)^{t}$

$t = \frac{ \ln(2.289) }{1.04}$

$t = 0.7965$

To the nearest year, t= year