Question

In 2012, the population of a city was 5.74 million. The exponential growth rate was 3.75% per year.

a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 8 million?
d) Find the doubling time.
a) The exponential growth function is P(t) =
where t is in terms of the number of years since 2012 and P(t) is the
population in millions.
(Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the
equation.)

Answer 1

a) To find the exponential growth function, we need to use the formula:
P(t) = P_0 (1 + r)^t
Where P(t) is the population at time t, P_0 is the initial population, r is the growth rate, and t is the time in years. We are given that P_0 = 5.74 million, r = 0.0375, and t is the number of years since 2012. Plugging these values into the formula, we get:
P(t) = 5.74 (1 + 0.0375)^t

b)2018-2012=6 so t=6
Then plugging that in we get
P(6)= 5.74(1+0.0375)^6= 7.158804867 you can estimate that to 7.16 if you want so we get 7.16million people.

(C) 8 = 5.74 (1 + 0.0375)^t to solve for t you flip the equation till you get t=9.0178
2012+9 and you get 2021

D)I don’t have time to write the formula and stuff but the doubling time is 18.828 years

Answer 2

a) P(t) = 5.74e^(.0375t)

b) P(6) = 5.74e^(.0375(6)) = about 7.19

million

c) 5.74e^(.0375t) = 8

t = about 8.85 years

d) e^(.0375t) = 2

.0375t = ln 2

t = (80 ln 2)/3 = about 18.48 years