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)
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<pre>
According to the given info, the formula for the fox population in the region after 2013 is

    F(n) = {{{17000*(1+0.05)^n}}} = {{{17000*1.05^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 = {{{17000*1.05^n}}};


divide both sides by 17000

    {{{25000/17000}}} = {{{1.05^n}}}

    {{{1.470588}}} = {{{1.05^n}}};


take logarithm base 10 of both sides

    log(1.470588) = n*log(1.05)


and express/calculate n

    n = {{{log((1.470588))/log((1.05))}}} = 7.90451.


Now round to the greater decimal number, as requested, to have the population of 27,000, for sure:


<U>ANSWER</U>.  After 8 years, approximately.
</pre>

Solved.


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If you want to see many other similar and different solved problems on population growth, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Population-growth-problems.lesson>Population growth problems</A> 

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Logarithms</U>".



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.