SOLUTION: Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1?
What is the size of the population at
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Question 187051: Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1?
What is the size of the population at the end of year 2?
What is the size of the population at the end of year 3?
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? Use a calculator to solve to x.
I am truly not even sure how to get started on this problem, any and all help would be greatly appreciated. Thanks
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
" initial size 100 grows at the rate of 8% per year forever" ---> =100\cdot\left(1.08\right)^{t})
What is the size of the population at the end of year 1?
=100\cdot\left(1.08\right)^{1})
=100\cdot\left(1.08\right))
=108)
Ans: 108 people at end of yr 1
------------------------------------------------------
What is the size of the population at the end of year 2?
=100\cdot\left(1.08\right)^{2})
=100\cdot\left(1.1664\right))
=116.64)
Ans: 116 people at end of yr 2
------------------------------------------------------
What is the size of the population at the end of year 3?
=100\cdot\left(1.08\right)^{3})
=100\cdot\left(1.259712\right))
=125.9712)
Ans: 125 people at end of yr 3
------------------------------------------------------
What is the size of the population at the end of year n?
=100\cdot\left(1.08\right)^{n})
------------------------------------------------------
find the number of years x that it would take for our population to reach 200?
^{t})
^{t})
=\log_{10}\left(\left(1.08\right)^{t}\right))
=t\cdot\log_{10}\left(1.08\right))
}{\log_{10}\left(1.08\right)}=t)
}{\log_{10}\left(1.08\right)})
Ans: takes about 9 yrs for pop. to reach 200 people
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