Answer:
(a) k=0.06217
(b) [tex]P=264036e^{0.06217t}[/tex]
(c) 556,755 is the population in 2012
Step-by-step explanation:
Population increased from 264,036 in 1990 to 491,675 in 2000.
Let assume , year 1990 as t=0
When t=0, population P = 264,036
When t=10, population P = 491,675
Exponential growth equation is P=P_0e^(kt)
[tex]P_0[/tex] is the initial population when t=0
So [tex]P_0= 264,036[/tex]
When t=10, population P = 491,675
Plug in all the values and find out k
[tex]491675 = 264036 e^{k*10}[/tex]
Divide both sides by 264036
[tex]\frac{491675}{264036}=e^{k*10}[/tex]
To remove 'e' we take ln on both sides
[tex]ln(\frac{491675}{264036})=lne^{10k}[/tex]
[tex]ln(\frac{491675}{264036})=10kln(e)[/tex]
The value of ln(e) = 1
[tex]ln(\frac{491675}{264036})=10k[/tex]
Divide both sides by 10
k=0.06217
Exponential growth equation is [tex]P=P_0e^{kt}[/tex]
We know [tex]P_0= 264,036[/tex]
Replace the value of k
[tex]P=264036e^{0.06217t}[/tex]
Now , we find the population in 2012
For year 2012 , t= 12
So we plug on 12 for t and solve for P
[tex]P=264036e^{0.06217*12}[/tex]
P = 556755.09504
556,755 is the population in 2012
