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kotykmax [81]
4 years ago
10

A town has a population of 17000 and grows at 3% every year. To the nearest year, how long will it be until the population will

reach 20400
Mathematics
1 answer:
Mumz [18]4 years ago
6 0

Answer:

The population will reach 20,400 after 6 years.

Step-by-step explanation:

Exponential function:

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

y(t)= Population after t years

y_0 = initial population

r= rate of grow

t= time.

A town has a population of 17,000 and grows at a rate 3% every year.

y(t)= 20,400, y_0 = 17,000, r=3%=0.03, t=?

20,400=17,000(1+0.03)^t

\Rightarrow \frac{20,400}{17,000}=(1.03)^t

\Rightarrow \frac{102}{85}=(1.03)^t

Taking ln function both sides

\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|

\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|

\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}

⇒ t = 6 year.

The population will reach 20,400 after 6 years.

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