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solve applications of exponential functions

label Mathematics
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In 2005 the population of a certain city was $19,625. If the relative growth rate has been 6.2% since 1986. What was the population of the city in 1986?

Apr 3rd, 2015

$19625=x*e^(0.062*19), t=2005-1986=19 years

x=$6042.42

Apr 3rd, 2015

there shouldn't be a dollar sign in front of the answer, sorry about that. 

Apr 3rd, 2015

I want to know how you derived at the answer.

Apr 3rd, 2015

19625=x*e^(0.062*19), t=2005-1986=19 years

x=19625/(e^0.062*19)=19625/3.247872=6042.42..........do this if you have a calculator

Or you can do

x=19625/(e^0.062*19), take ln of both sides, lnx=ln(19625/e^1.178). lnx=ln19625-lne^1.178, lne^1.178=1.178.

So lnx=1.178*ln19625.....x=e^(1.178*ln19625).....this is the more complicated way of ding it.....


Apr 3rd, 2015

Thank you so very much great help.


Apr 3rd, 2015

No problem glad you understand the question now . 

Apr 3rd, 2015

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Apr 3rd, 2015
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Apr 3rd, 2015
Sep 24th, 2017
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