Question
A function models a linear relationship between the mileage (miles driven) for a truck and the number of years since it was purchased. Currently, the truck’s mileage is 107,500, and it has been driven at a rate of 15,000 miles per year since it was purchased 7 years ago.
What is the initial value of the mileage function, in miles?
0 miles
7 miles
2,500 miles
10,700 miles
What is the initial value of the mileage function, in miles?
0 miles
7 miles
2,500 miles
10,700 miles
Answers
GPT-4o mini
To find the initial value of the mileage function, we can use the information given about the truck’s mileage and the rate at which it has been driven.
The truck has been driven for 7 years at a rate of 15,000 miles per year. Thus, the total mileage accrued over those 7 years is:
\[ 15,000 \text{ miles/year} \times 7 \text{ years} = 105,000 \text{ miles}. \]
Given that the current mileage is 107,500 miles, we can find the initial mileage (mileage at the time of purchase) by subtracting the total mileage driven from the current mileage:
\[ \text{Initial mileage} = \text{Current mileage} - \text{Mileage driven} \]
\[ \text{Initial mileage} = 107,500 \text{ miles} - 105,000 \text{ miles} = 2,500 \text{ miles}. \]
Therefore, the initial value of the mileage function is **2,500 miles**.
The truck has been driven for 7 years at a rate of 15,000 miles per year. Thus, the total mileage accrued over those 7 years is:
\[ 15,000 \text{ miles/year} \times 7 \text{ years} = 105,000 \text{ miles}. \]
Given that the current mileage is 107,500 miles, we can find the initial mileage (mileage at the time of purchase) by subtracting the total mileage driven from the current mileage:
\[ \text{Initial mileage} = \text{Current mileage} - \text{Mileage driven} \]
\[ \text{Initial mileage} = 107,500 \text{ miles} - 105,000 \text{ miles} = 2,500 \text{ miles}. \]
Therefore, the initial value of the mileage function is **2,500 miles**.