Question 1116381: A town has a population of 3500 people at time t = 0. In each case, write an
equation for the population P, of the town as a function of year t.
a) the population size increases by 80 per year.
I believe this answer to be P=3500 +80t
b)The population size increases by 3.2 percent per year.
I believe this answer to be P=3500(1.032)^t
c) The population increases continuously at a rate of 2.65% per year.
I believe this answer to be P=3500e^0.0265t
d) Find the doubling time for each of the functions you found above:
I believe a is 30.6 years, b is 67.8 years, but I do not know how to find the doubling time of d.
Please help! Thank you
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a is correct
b is also correct
c is correct
for d, with continuous
7000=3500e^(0.0265t)
2=e^(0.0265t)
ln2=0.0265t
0.693=0.0265t
t=26.25 years
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for d, with 3.2 per cent
2=1.032^t
ln both sides
ln 2=t ln (1.032)
divide both sides by ln (1.032)
t=22.0 years
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for d, with an increase of 80 per year
doubles after 3500/80=43.75 years
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