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 .

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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 .

Mathematics
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Okay...
You're given the fact they want to model the population growth as\[f(t)=a+b \sqrt{t}\]
You're told that, at time 0, f(0)=2000, so\[f(0)=2000=a + b \sqrt{0}=a\]

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and at time t=16, you have\[f(16)=18000=b \sqrt{16}=4b\]so b = 18000/4 = 4500
\[f(t)=2000+4500\sqrt{t}\]
sorry - I went too quickly and made a mistake typing out
its okay, thanks man i really appreciate it.
a = 2000 as above. Scrap the rest and go from here...
\[f(16)=a+b \sqrt{t}=2000+b \sqrt{16}=2000+4b=18000\]
so\[b=\frac{18000-2000}{4}=4000\]
So \[f(t)=2000+4000\sqrt{t}\]
Are you okay with this?
yea I am thanks man
feel free to 'fan' me ;)
ok i will

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