Question

1. The price of a particular model of car is $18000 today and rises with time at a constant rate of$900 per year. b) Make a scatterplot with line of best fit. Screenshot in the scatterplot. c) Write a linear equation that models this situation. Time is the explanatory variable, and Price is the response variable. d) Explain what the slope means in this context of the problem. Be sure to use units and to write a clear sentence. e) How much will the car cost in 4.5 years? f) When will the car double in price? g) Do you believe this result or are you skeptical?

Answer 1

a) Let x represent the time in years and let y represent the price of the car. For years 0 through 8, we have the following table:

b) With the table from the previous part, we have the following scatterplot:

c) The equation that represents this scenario given the information on the problem is the following:

`Y=18000+900X`

d) In this case, the slope inicates the quantity of the price of the car that will increase for each unit of time, in this case, each year.

e)To find out how much the car will cost in 4.5 years, we can make X = 4.5 to get the following:

`Y=18000+900(4.5\text{\rparen}=22050`

thus, the car will cost $22050 in 4.5 years.

f)If we want to know when will the price of the car be twice the original price, we can make y = 2(18000)=36000 and solve for x:

`\begin{gathered} 36000=18000+900X \\ \Rightarrow X=(18000)/(900)=20 \\ X=20 \end{gathered}`

therefore, in 20 years the price of the car will be twice the original price.

g)These statements can be true with certain degree of confidence since the relationship between the time and the price of the car is linear.