Final answer:
The function modeling Marco's distance to the Grand Canyon as a function of time is y = -50x + 400, indicating he is decreasing his distance by 50 miles for every hour he drives, and started his journey 400 miles away from the Grand Canyon.
Step-by-step explanation:
The student's question involves creating a linear function to model the change in distance to the Grand Canyon over time.
Since Marco's distance decreases by 150 miles every 3 hours, we can find the rate of change in distance per hour. After 4 hours, the distance to the Grand Canyon is 200 miles.
To find the linear function, we can assume that the function is of the form y = mx + b, where y is the distance in miles, x is the time in hours, m is the rate of change of distance with respect to time, and b is the initial distance from the Grand Canyon.
First, we calculate m, the rate of distance decrease per hour:
m = (distance decrease) / (time period)
= 150 miles / 3 hours
= 50 miles/hour
Because the distance is decreasing, m is negative, so m = -50 miles/hour.
Next, we use the information that after 4 hours Marco is 200 miles away to find b. Plugging the values into y = mx + b:
- 200 = -50(4) + b
- 200 = -200 + b
- b = 400
The initial distance Marco was from the Grand Canyon when he started his drive was 400 miles. Therefore, the function modeling Marco's distance to the Grand Canyon over time is y = -50x + 400.