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

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