## anonymous 5 years ago i have a question i was just wondering if anyone would be able to help me get started. Suppose a population is growing in a profile which is shaped like the function y= f(x)= the squareroot of x, so demographers have decided to model this population growth by the equation p= a+b(squareroot of t) , and have determined that initially (at relative time ) the population was 2000 and 16 years later the population was 18000. Determine values for the parameters a and b .

1. anonymous

Okay...

2. anonymous

You're given the fact they want to model the population growth as$f(t)=a+b \sqrt{t}$

3. anonymous

You're told that, at time 0, f(0)=2000, so$f(0)=2000=a + b \sqrt{0}=a$

4. anonymous

and at time t=16, you have$f(16)=18000=b \sqrt{16}=4b$so b = 18000/4 = 4500

5. anonymous

$f(t)=2000+4500\sqrt{t}$

6. anonymous

sorry - I went too quickly and made a mistake typing out

7. anonymous

its okay, thanks man i really appreciate it.

8. anonymous

a = 2000 as above. Scrap the rest and go from here...

9. anonymous

$f(16)=a+b \sqrt{t}=2000+b \sqrt{16}=2000+4b=18000$

10. anonymous

so$b=\frac{18000-2000}{4}=4000$

11. anonymous

So $f(t)=2000+4000\sqrt{t}$

12. anonymous

Are you okay with this?

13. anonymous

yea I am thanks man

14. anonymous

feel free to 'fan' me ;)

15. anonymous

ok i will