Question

Type the correct answer in each box. Use numerals instead of words.

Harry buys a boat in 2010. He plans on selling it in 2020. In 2010, the boat costs $20,000. The value of the boat depreciates over time
as is shown in the graph below, where the y-axis represents the value of the boat, in dollars, and the x-axis represents the number of
years since 2010.

Answer 1

The initial value of the boat was $20,000

The percent decrease per year of the value of the boat is 10%.

The interval on which the value of the boat is decreasing while Harry has it is (0,10)

Explanation:

It is given that the boat costs $20,000 in 2010 when x = 0. So, the initial value of the boat was $20,000.

Next, find the percent decrease per year of the value of the boat. Consider the general form of an exponential equation, y = a(b)x, where a is the initial value of the boat, b is the base of the exponent, x is the number of years after 2010, and y is the value of the boat, in dollars.

Consider the point (1 , 18,000) which lies on the graph of this situation. Substitute x = 1, y = 18,000, and a = 20,000 into the exponential equation and isolate b.

Recall that for exponential decay, b = 1 - r where r represents the decay rate. Substitute b = 0.9 into this equation and solve for r.

So, the decay rate is 0.1, and the percent decrease per year of the value of the boat is 10%.

Harry bought the boat in 2010, and plans on selling it after 10 years in 2020. Therefore, the interval on which the value of the boat is decreasing while Harry has it is [0, 10].