Answer:
The population will reach 39,400 after 17 years.
Step-by-step explanation:
Given that, The population grows at a rate 4%. The population of the town is 20,000 at a certain time.
Exponential function:
[tex]y(t)=y_0(1+r)^t[/tex]
y(t) = The population after t years
[tex]y_0[/tex] = Initial population.
r = Rate of grow
t = Time.
y(t)= 39400, [tex]y_0[/tex] = 20,000, r= 4%=0.04, t=?
[tex]39400=20000(1+0.04)^t[/tex]
[tex]\Rightarrow \frac{39400}{20000}=(1.04)^t[/tex]
[tex]\Rightarrow \frac{197}{100}=(1.04)^t[/tex]
Taking ln both sides
[tex]\Rightarrow ln|\frac{197}{100}|=ln|(1.04)^t|[/tex]
[tex]\Rightarrow ln|\frac{197}{100}|=t\ ln|(1.04)|[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{197}{100}|}{ln|(1.04)|}[/tex]
[tex]\Rightarrow t\approx 17[/tex]
The population will reach 39,400 after 17 years.
