# 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?

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Exponential models
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 $$\displaystyle{y}={15},{540}{\left({0.95}\right)}^{{x}}$$ ### Relevant Questions asked 2021-05-26 You open a bank account to save for college and deposit$400 in the account. Each year, the balance in your account will increase $$5\%$$. a. Write a function that models your annual balance. b. What will be the total amount in your account after 7 yr? Use the exponential function and extend the table to answer part b.
Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth $25,000, and its value decreases by 15% each year; 6 years. asked 2021-02-21 Use the exponential growth model, $$A=A_0e^{kt}$$. In 1975, the population of Europe was 679 million. By 2015, the population had grown to 746 million. Solve, a. Find an exponential growth function that models the data for 1975 through 2015. b. By which year, to the nearest year, will the European population reach 800 million? asked 2020-11-08 Often new technology spreads exponentially. Between 1995 and 2005, each year the number of Internet domain hosts was 1.43 times the number of hosts in the preceding year. In 1995, the number of hosts was 8.2 million. (a) Explain why the number of hosts is an exponential function of time. The number of hosts grows by a factor of -----? each year, this is an exponential function because the number is growing by ------? decreasing constant increasing multiples. (b) Find a formula for the exponential function that gives the number N of hosts, in millions, as a function of the time t in years since 1995. (c) According to this model, in what year did the number of hosts reach 49 million? asked 2020-11-11 Use a calculator with a $$y^x$$ key or a key to solve: India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the population of China, by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function $$f(x)=574(1.026)^x$$ models the population of India, f(x), in millions, x years after 1974. a. Substitute 0 for x and, without using a calculator, find India’s population in 1974. b. Substitute 27 for x and use your calculator to find India’s population, to the nearest million, in the year 2001 as modeled by this function. c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function. asked 2021-03-07 This problem is about the equation dP/dt = kP-H , P(0) = Po, where k > 0 and H > 0 are constants. If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth. Problem: find acondition on H, involving $$\displaystyle{P}_{{0}}$$ and k, that will prevent solutions from growing exponentially. asked 2021-02-06 A computer valued at$1500 loses 20% of its value each year. a. Write a function rule that models the value of the computer. b. Find the value of the computer after 3 yr. c. In how many years will the value of the computer be less than $500? Set your exponential function equal to$500 and solve or extend your table to determine the answer to part c.
Use the exponential growth model $$A=A_0e^{kt}$$ to solve: In 2000, there were 110 million cellphone subscribers in the United States. By 2010, there were 303 million subscribers