Andreas buys a new ailboat fo $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?

Andreas buys a new ailboat fo $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?

Question
Exponential models
asked 2021-01-19
Andreas buys a new ailboat fo $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?

Answers (1)

2021-01-20
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
\(\displaystyle{y}={15},{540}{\left({0.95}\right)}^{{x}}\)
0

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