SOLUTION: A midwestern city had a population of 650,000 in 2010. The population, which follows the exponential model, decreased 4.65% per year. Show all work! a. Find the exponential fu

Question 1157956: A midwestern city had a population of 650,000 in 2010. The population, which follows the exponential model, decreased 4.65% per year. Show all work!
a. Find the exponential function that models the population after t years.
(Remember to change the rate to a negative decimal.)
b. What is the projected population in the year 2020?
c. In how many years will the population be expected to be 300,000?
Answer by Amily_2190(27) (Show Source): You can put this solution on YOUR website!
a)Population decreased 4.65% per year; -4.65%= -.0465
To determine how much of the population remains per year, subtract 4.65%(-.0465) from the total population of 100% or 1.
1-.0465=.9535
t=# of years after 2010

Answer: P(t)= 650,000(.9535)^t

b) 2020-2010= 10 (2020 is 10 years after 2010, so t=10)
P(t)=650,000(.9535)^10 is approximately 403,757

c) 300,000= 650,000(.9535)^t
300,000/650,000=(.9535)^t
(Use logarithm to figure out t on calculator)
log base .9535 of 300,000/650,000 equals t

t is approximately 16.2 years

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