From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008. a) Exponential growth or decay: b) Identify the initial amount: c) Identify the growth/decay factor: d) Write an exponential function to model the situation: e) "Do" the problem.

Question
Exponential growth and decay
asked 2021-02-03
From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
a) Exponential growth or decay:
b) Identify the initial amount:
c) Identify the growth/decay factor:
d) Write an exponential function to model the situation:
e) "Do" the problem.

Answers (1)

2021-02-04
a)Since the population decreases, it is an exponential decay.
b)If the year 2000 corresponds to t=0t=0, then the initial amount is 2,950,000.
c)The decay rate is r=2.5%. Since the decay factor is given by 1−r, we have 1 - 0.025 or 0.975.
d)The exponential decay is given by y=a(1−r)x where aa is the initial amount and 1−r is the decay factor. Hence, we have:
y=2,950,000(0.975)x where x is the number of years after 2000.
e)Year 2008 corresponds to x=8 so we have: y=2,950,000(0.975)8
y≈2,409,123
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