Question 1194681: The fox population in a certain region has a relative growth rate of 5% per year. It is estimated that the population in 2013 was 17,000.
1. After how many years will the fox population reach 25,000?
(Round your answer to one decimal place)
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! The fox population in a certain region has a relative growth rate of 5% per year.
It is estimated that the population in 2013 was 17,000.
1. After how many years will the fox population reach 25,000?
(Round your answer to one decimal place)
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According to the given info, the formula for the fox population in the region after 2013 is
F(n) =  =  ,
where n is the year after 2013.
To find the year "n" under the problem's question, we write this equation for the furure fox population
25000 = ;
divide both sides by 17000
 = 
 = ;
take logarithm base 10 of both sides
log(1.470588) = n*log(1.05)
and express/calculate n
n =  = 7.90451.
Now round to the greater decimal number, as requested, to have the population of 27,000, for sure:
ANSWER. After 8 years, approximately.
Solved.
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If you want to see many other similar and different solved problems on population growth, look into the lesson
- Population growth problems
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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