This question is incomplete, the complete question is;
A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
a) Find the slopes of the secant lines corresponding to the given intervals of t.
1) [ 0, 40 ]
11) [ 10, 20 ]
111) [ 20, 30 ]
b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
Answer:
a)
1) for [ 0, 40 ], slope is 96
11) for [ 10, 20 ], slope is 86.3
111) for [ 20, 30 ], slope is 116.4
b) the student's walking pace is 101 per min
Explanation:
Given the data in the question;
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
SLOPE OF SECANT LINES
1) [ 0, 40 ]
slope = ( 7,128 - 3,288 ) / ( 40 - 0
= 3840 / 40 = 96
Hence slope is 96
11) [ 10, 20 ]
slope = ( 5,522 - 4,659 ) / ( 20 - 10 )
= 863 / 10 = 86.3
Hence slope is 86.3
111) [ 20, 30 ]
slope = ( 6,686 - 5,522 ) / ( 30 - 20 )
= 1164 / 10 = 116.4
Hence slope is 116.4
b)
Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .
Since this is recorded after 3:00 pm
{ 3:20 - 3:00 = 20 }
so t = 20 min
so by average;
we have ( [ 10, 20 ] + [ 20, 30 ] ) /2
⇒ ( 86.3 + 116.4 ) / 2
= 202.7 /2
= 101.35 ≈ 101
Therefore, the student's walking pace is 101 per minutes