Question 1140192
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There are good reasons in certain cases to use exponential growth using the natural base e.  But in this simple example it greatly complicates the solution.<br>
The population grew from 1000 to 1400 in 1 day; the daily growth factor is 1400/1000 = 1.4.  So the equation for the number of mosquitoes after n days is<br>
{{{P(n) = 1000(1.4)^n}}}<br>
(1) For the population after 3 days, evaluate the equation for n=3:
{{{P(3) = 1000(1.4)^3 = 2744}}}<br>
The population is about 2744 after 3 days.<br>
(2) To find the number of days for the population to reach 70,000, set P=70000 and solve for n.<br>
{{{70000 = 1000(1.4)^n}}}
{{{70 = 1.4^n}}}
{{{log((70)) = n*log((1.4))}}}
{{{n = log((70))/log((1.4))}}} = 12.626585 to several decimal places<br>
It takes about 12.6 days for the population to reach 70,000.