Andreas buys a new sailboat for $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation? F. y=15,540(1.05)x G. y=15,540(0.95)x H. y=−15,540(0.95)x J. y=−15,540(1.05)x

Question

Andreas buys a new sailboat for $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?   F. y=15,540(1.05)x  G. y=15,540(0.95)x  H. y=−15,540(0.95)x  J. y=−15,540(1.05)x

Natalie Yamamoto · Accepted Answer

The exponential decay model is given by,  y=a(1−r)t where,  a is the initial amount  r is the decay rate  t is the time period  (1−r) is the decay factor  From the given data the following equation is formulated.  y=15,540(1−0.05)x  y=15,540(0.95)x  Therefore, the correct option is G.

Mary Herrera · Accepted Answer

We have to use a straight-line depreciation model here as the asset depreciates by the same amount each year. The model is given below.  y=p(1−r)x  In the model, p is the purchase value of the asset, r is the yearly rate of depreciation, and x is the number of years that the asset has been held for.   Using the information in the question, p=$15540 and r=0.05.  So, the model is:  y=15540(1−0.05)x=15540(0.95)x  So, the correct option is b.

user_27qwe · Accepted Answer

Given, initial price of sailboat, P0=$15,540 Price of the sailboat depreciate by 5% each year. Thus, price of sailboat after 1 year =P0−0.05P0=0.95P0 Similarly, price of sailboat after 2 years =0.95P0−0.05(0.95P0) =0.95P0(1−0.05) =(0.95)2P0 Therefore, price of sailboat after x years =(0.95)xP0 =15,540(0.95)x Answer: The exponential model for the price of boat (y) after x years is y=15,540(0.95)x

Andreas buys a new sailboat for $15,540. He estimates that

Answered question

Answer & Explanation

New Questions in Algebra I