SOLUTION: this exercise uses the population growth model. A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 1

Algebra ->  Equations -> SOLUTION: this exercise uses the population growth model. A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 1      Log On


   

Question 1157134: this exercise uses the population growth model.
A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 19,000.
(a) What was the initial size of the bird population? (Round your answer to the nearest whole number.)
______birds
(b) Estimate the bird population 7 years from now. (Round your answer to the nearest whole number.)
__________birds
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

(a)  Original population was  19000/(2^(25/10)) = 19000%2F2%5E2.5 = 3359 (rounded).   ANSWER


         2.5 here is the number of doubling periods in 25 years.



(b)  Population in 7 years from now will be  19000*2^(7/10) = 19000%2A2%5E0.7 = 30866  (rounded).    ANSWER


         7%2F10 = 0.7  here is the number of doubling periods in 7 years.

Solved.

================

Added after seening the post by @Boreal. 

    In this problem, all the data are presented in terms of a doubling period.

    It assumes, that the entire solution should be made in these terms.

    It really can be done in terms of doubling period, and a good style ASSUMES that it will be done in these terms.

    Transition to another forms of an exponential model is possible, in principle, but it means 

    performing UNNECESSARY calculations, where you can make errors and may lose a precision in your calculations.


   
        Therefore, I strongly recommend to solve such problems in terms of doubling periods.



    Again: when the input data are in terms of doubling period, it is logically right way to make all calculations in this frame.


    Doing another way, you perform TONS of unnecessary calculations and create unnecessary problems for yourself

    and do everything to lower your reputation.



Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
A=Aob^x general form.
A/Ao=2=(1+r)^10 years
ln 2=10 ln (1+r)
ln(1+r)=0.0693
raise to e power
1+r=1.071
rate is 7.1% growth per year
19000=Ao(1.071)^25
19000=5.556Ao
Ao=3419.92 or 3420
in 7 years 19000*1.071^7=30,710
same for 34120*1.071^32