In 2004, the population of butterflies in West Fremont is 60,000, and growing at a rate of 1.4% each year. If the rate of population growth remains constant, determine the year in which the population will reach 240,000?

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Answer 1 · 2016-02-08T16:41:12

#99.713" " #years

Like in financial interest we have #P(1+1.4/100)^n#

In this case it is :#" " 60000(1+1.4/100)^n=240000#

So#" " (1+1.4/100)^n=240/60=24/6=4#

Taking logs

#n ln(101.4/100)=ln(4)#

#n=ln(4)/(ln(101.4/100))" "=" "(ln(4))/(ln(101.4)-ln(100))=99.713#
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#color(blue)("Comment: ")#

This model does not allow for any deaths of the parents or caterpillars.