The number of individuals arrested A(t) for driving under the influence as a fun
ID: 2869850 • Letter: T
Question
The number of individuals arrested A(t) for driving under the influence as a function of their age t is indicated in Table 1. Use the data in Table 1 to:
(I) Estimate the average rate of change in the number of arrests (per 100,000 drivers) for driving under the influence between the ages of 18 and 26.
(II) Estimate the instantaneous rate of change at the age of 40 and interpret your answer.
Table I
Age
(years)
Number of Arrests
(per 100,000)
14
113.00
16
308.77
18
421.32
20
485.32
22
519.13
24
534.54
26
537.99
28
533.67
30
524.25
32
511.47
34
496.52
36
480.17
38
462.97
40
445.30
42
427.40
44
409.45
46
391.59
48
373.89
50
356.41
52
339.18
54
322.23
56
305.57
58
289.21
60
273.14
Answers:
Age
(years)
Number of Arrests
(per 100,000)
14
113.00
16
308.77
18
421.32
20
485.32
22
519.13
24
534.54
26
537.99
28
533.67
30
524.25
32
511.47
34
496.52
36
480.17
38
462.97
40
445.30
42
427.40
44
409.45
46
391.59
48
373.89
50
356.41
52
339.18
54
322.23
56
305.57
58
289.21
60
273.14
Explanation / Answer
1)average=(537.99-421.32)/(26-18)
=14.58
2)at 40
(427.40-462.97)/(42-38)
=-8.893
option A
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