Question

A town has a population of 20000 and grows at 4% every year. How long will it be until the population will reach 39400?

Answer 1

Answer:

The population will be 39400 in approximately 17 years

Step-by-step explanation:

The increase in population after t years is given by the formula

$P_t = P_0(1+r)^t$

Here

P_0 is the initial population

r is the growth rate and t is time in years

So far we know,

P_0 = 20000

r = 4%

P_t = 39400

Putting the values in the formula

$39400 = 20000(1+0.04)^t\\39400 =20000(1.04)^t\\\frac{39400}{20000} = (1.04)^t\\1.97 = (1.04)^t$

Taking natural log on both sides

$ln |(1.04)^t| = ln |1.97|\\t\ ln\ |1.04| = ln\ |1.97|\\t = \frac{ln\ 1.97}{ln\ 1.04}\\t = 17.287\\t \approx 17$

Hence,

The population will be 39400 in approximately 17 years