Ann's ride , a piecewise function
Ann went on a 10 hour bicycle trip. The table shows selected points on the graph.
t-0-1-4-7-10
d (t)- 0-3-5-5-10.
Write a function d(t) for her total distance traveled in miles in terms of the time in hours. Please help!
To write a function d(t) for Ann's total distance traveled in miles in terms of the time in hours, we can use a piecewise function.
From the table, we can observe that for the first hour (t = 0), Ann starts at 0 miles. From t = 0 to t = 1, Ann travels 3 miles. From t = 1 to t = 4, she travels 2 miles. From t = 4 to t = 7, she stays at 5 miles. Finally, from t = 7 to t = 10, she travels 5 miles.
To represent this information in a piecewise function, we can write it as follows:
d(t) = {
0, for 0 ≤ t < 1,
3(t - 1), for 1 ≤ t < 4,
5, for 4 ≤ t < 7,
5(t - 7), for 7 ≤ t < 10,
10, for t ≥ 10.
}
Please note that the function represents the total distance traveled at each time value, so it is not a continuous function and has different expressions for different time intervals.
To find the function d(t) for Ann's total distance traveled in miles in terms of time in hours, we can use the given table of values.
First, let's analyze the given points on the graph:
t = 0, d(t) = 0
t = 1, d(t) = 3
t = 4, d(t) = 5
t = 7, d(t) = 5
t = 10, d(t) = 10
From the given points, we can observe that the distance traveled by Ann remains constant from 1 to 4 hours and from 4 to 7 hours.
For t in the range 0 ≤ t < 1, Ann's distance traveled is 0 miles.
For t in the range 1 ≤ t < 4, Ann's distance traveled is 3 miles. This represents the constant distance Ann traveled during this time interval.
For t in the range 4 ≤ t < 7, Ann's distance traveled remains at 5 miles. This is another constant distance that Ann covered during this time interval.
Finally, for t in the range 7 ≤ t ≤ 10, Ann's distance traveled is 10 miles, as shown in the table.
Based on this analysis, we can write the piecewise function for Ann's total distance traveled, d(t), as follows:
d(t) = {
0 if 0 ≤ t < 1,
3 if 1 ≤ t < 4,
5 if 4 ≤ t < 7,
10 if 7 ≤ t ≤ 10
}
Therefore, the function d(t) for Ann's total distance traveled in miles in terms of time in hours is given by the piecewise function mentioned above.