Question

# 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 and decay
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.

2021-05-19
a)Since the population decreases, it is an exponential decay.
b)If the year 2000 corresponds to t=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 $$\displaystyle{y}={a}{\left({1}−{r}\right)}^{{x}}$$ where aa is the initial amount and 1−r is the decay factor. Hence, we have:
$$\displaystyle{y}={2},{950},{000}{\left({0.975}\right)}^{{x}}$$ where xx is the number of years after 2000.
e)Year 2008 corresponds to x=8 so we have:
$$\displaystyle{y}={2},{950},{000}{\left({0.975}\right)}^{{8}}$$
y≈2,409,123