Create a piecewise function of the following scenario where D(t) is the total distance walked in miles as a function of time T (in minutes) You begin a walk from your home at a fast pace of 6 miles per hour for 30 minutes. You rest for 15 minutes, and then you continue walking at a leisurely pace of 1 mile per hour for 30 minutes."
I have D(t)=1/10t when 0<=t<=30
D(t)=3
i need help with the last one of 45<t<=75
i initially put in 3+1/60t but that is incorrect
D(t) =
1/10 t for 0 <= t <= 30
3 for 30 < t <= 45
3 + 1/60 (t-45) for 45 < t <= 75
Looks good to me. Why do you say it is wrong?
To find the function for the interval 45 < t <= 75, we need to consider the scenario where you continue walking at a leisurely pace of 1 mile per hour for 30 minutes.
Since the walking speed is 1 mile per hour, in 30 minutes you will cover a distance of 1/2 mile (since 30 minutes is half an hour). Therefore, for this interval, you need to add an additional 1/2 mile to the total distance walked.
So, the function for 45 < t <= 75 can be written as:
D(t) = 3 + (1/10)t for 0 <= t <= 30
D(t) = 3 + (1/2) for 30 <= t <= 45
D(t) = ? for 45 <= t <= 75
To find the equation for the last interval, subtract the endpoint (45), find how much time has passed in that interval (t - 45), and multiply it by the walking speed (1/10). Then add that value to the total distance walked up until that point (3 + 1/2). The equation becomes:
D(t) = 3 + (1/2) + (1/10)(t - 45) for 45 <= t <= 75.
This function represents the total distance walked in miles as a function of time for the given scenario.