SOLUTION: The population of a certain city was 110,000 in 2014, and the observed doubling time for the population is 18 years.
(a) Find an exponential model
n(t) = n02t/a
for the popula
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Question 1157178: The population of a certain city was 110,000 in 2014, and the observed doubling time for the population is 18 years.
(a) Find an exponential model
n(t) = n02t/a
for the population t years after 2014.
n(t) =
(b) Find an exponential model
n(t) = n0ert
for the population t years after 2014. (Round your r value to four decimal places.)
n(t) =
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
exponential model is n(t) = ab^t
a = 110
n(t) = 220
t = 18
solve for b
you get:
220 = 110 * b^18
divide both sides of this equation by 110 to get
2 = b^18
take the 18th root of both sides of the equation to get:
2^(1/18) = b
solve for b to get:
b = 1.039259226...
store that in your calculator and then confirm by replacing b with that to get:
n(t) = 110 * (1.039259226...)^18 = 220.
your equation is:
n(t) = 110 * (1.039259226...)^t
here's a graph of that equation after replacing n(t) with y and t with x.
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