anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Okay...
anonymous
  • anonymous
You're given the fact they want to model the population growth as\[f(t)=a+b \sqrt{t}\]
anonymous
  • anonymous
You're told that, at time 0, f(0)=2000, so\[f(0)=2000=a + b \sqrt{0}=a\]

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

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