SOLUTION: Can someone please help me with this problem? If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population

Question 125456: Can someone please help me with this problem?
If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth?
My answer options are:
a.33.8 yrs
b.3.73 yrs
c.32.8 yrs
d.17.5 yrs
Please get back to me as soon as possible, I am homeschooled but on a deadline to get this finished, thanks!!!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth?
:
Let t = no. of years for this to occur
:
We know the population in 1 yr, we can multiply 350,000 by 1.0325,
therefore, the equation will be:
:
350000*(1.0325)^t = 1000000
:
Divide both sides by 350000
1.0325^t =
1.0325^t = 2.857
:
Use the nat log of both sides:
ln(1.0325^t) = ln(2.857)
:
The log equivalent of exponents:
t * ln(1.0325) = ln(2.857)
:
Find the nat log of both sides:
.03198t = 1.04977
t =
t = 32.8258 ~ 32.8
:
:
Check solution on a good calc; enter 350000 * l.0325^32.8 = 999222 ~ 1000000
:
You can try the other solutions and see which one is closest to 1,000,000
~
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