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

Question

asked Aug 11, 2021 183k views

1 Answer

Zeljko · Answer 1 · 2021-08-16T23:55:35+0000

Answer:

The population will reach 39,400 after 17 years.

Explanation:

Given that, The population grows at a rate 4%. The population of the town is 20,000 at a certain time.

Exponential function:

y(t)=y_0(1+r)^t

y(t) = The population after t years

y_0 = Initial population.

r = Rate of grow

t = Time.

y(t)= 39400,
y_0 = 20,000, r= 4%=0.04, t=?

39400=20000(1+0.04)^t

$\Rightarrow (39400)/(20000)=(1.04)^t$

$\Rightarrow (197)/(100)=(1.04)^t$

Taking ln both sides

$\Rightarrow ln|(197)/(100)|=ln|(1.04)^t|$

$\Rightarrow ln|(197)/(100)|=t\ ln|(1.04)|$

$\Rightarrow t= (ln|(197)/(100)|)/(ln|(1.04)|)$

$\Rightarrow t\approx 17$

The population will reach 39,400 after 17 years.