The population of collin county, which follows the exponential growth model, increased from 264,036 in 1990 to 491,675 in 2000.a. find the exponential rate, kb. write the exponential growth. c. what should the population be in 2012?

(a) k=0.06217

(b)

(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)

is the initial population when t=0

So

When t=10, population P = 491,675

Plug in all the values and find out k

Divide both sides by 264036

To remove 'e' we take ln on both sides

The value of ln(e) = 1

Divide both sides by 10

k=0.06217

Exponential growth equation is

We know  

Replace the value of k

Now , we find the population in 2012

For year 2012 , t= 12

So we plug on 12 for t  and solve for P

P = 556755.09504

556,755 is the population in 2012