Given,

Initial price of sailboat, \(\displaystyle{P}_{{0}}=\${15},{540}\)

Price of the sailboat depreciate by 5% each year.

Thus, price of sailboat after 1 year \(\displaystyle={P}_{{0}}-{0.05}{P}_{{0}}={0.95}{P}_{{0}}\)

Similarly, price of sailboat after 2 years \(\displaystyle={0.95}{P}_{{0}}-{0.05}{\left({0.95}{P}_{{0}}\right)}\)

\(\displaystyle={0.95}{P}_{{0}}{\left({1}-{0.05}\right)}\)

\(\displaystyle={\left({0.95}\right)}^{{2}}{P}_{{0}}\)

Therefore, price of sailboat after x years \(\displaystyle={\left({0.95}\right)}^{{x}}{P}_{{0}}\)

\(\displaystyle={15},{540}{\left({0.95}\right)}^{{x}}\)

Answer:

Then exponential model for the price of boat (y) after x years is

\(\displaystyle{y}={15},{540}{\left({0.95}\right)}^{{x}}\)

Initial price of sailboat, \(\displaystyle{P}_{{0}}=\${15},{540}\)

Price of the sailboat depreciate by 5% each year.

Thus, price of sailboat after 1 year \(\displaystyle={P}_{{0}}-{0.05}{P}_{{0}}={0.95}{P}_{{0}}\)

Similarly, price of sailboat after 2 years \(\displaystyle={0.95}{P}_{{0}}-{0.05}{\left({0.95}{P}_{{0}}\right)}\)

\(\displaystyle={0.95}{P}_{{0}}{\left({1}-{0.05}\right)}\)

\(\displaystyle={\left({0.95}\right)}^{{2}}{P}_{{0}}\)

Therefore, price of sailboat after x years \(\displaystyle={\left({0.95}\right)}^{{x}}{P}_{{0}}\)

\(\displaystyle={15},{540}{\left({0.95}\right)}^{{x}}\)

Answer:

Then exponential model for the price of boat (y) after x years is

\(\displaystyle{y}={15},{540}{\left({0.95}\right)}^{{x}}\)