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 .

Question

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 .

anonymous · Answer

Okay...

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

its okay, thanks man i really appreciate it.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Are you okay with this?

anonymous · Answer

yea I am thanks man

anonymous · Answer

feel free to 'fan' me ;)

anonymous · Answer

ok i will