A vehicle is traveling away from a town at a fixed rate. After 1 hours, the vehicle is 200 miles from the town. After 4 hours, the vehicle is 395 miles from the town. Which function represents the distance, , between the vehicle and the town after hours?
Correct Answer: D
Explanation:
Because the vehicle is traveling away from the town at a fixed rate, the distance can be modeled by a linear function: where: and We are given two points: and These mean: After hour, the vehicle is miles away. After hours, the vehicle is miles away. First, find the rate of change: So the vehicle is moving away from the town at a rate of: Now the function has the form: Use the point to find : Therefore, the function is: Check using :
Question 2
The number of people auditioning for a game show is expected to be 4 times the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A represents the number of people expected to audition this year. Which quantity represents the number of people expected to audition this year, given that 330 people auditioned last year?
Correct Answer: B
Explanation:
We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year. Let: t=number of people who auditioned last year and A(t)=number of people expected to audition this year Since this year’s number is 4 times last year’s number, the function is: A(t)=4t The question says that 330 people auditioned last year, so: t=330 Now substitute 330 into the function: A(330)=4(330) A(330)=1320 So, the correct function notation is: A(330)=1,320 This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.
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