After Julia had driven for half an hour, she was 155 miles from Denver. After driving 2 hours, she was 260 miles from Denver. Assume that Julia drove at a constant speed. Let f be a function that gives Julia's distance in miles from Denver after having driven for t hours. a. Determine a rule for the function f. b. Interpret f'(500). Calculate f'(500). c. Determine a rule for f'.

vangstosiis

vangstosiis

Answered question

2022-07-30

After Julia had driven for half an hour, she was 155 miles from Denver. After driving 2 hours, she was 260 miles from Denver. Assume that Julia drove at a constant speed. Let f be a function that gives Julia's distance in miles from Denver after having driven for t hours.
a. Determine a rule for the function f.
b. Interpret f'(500). Calculate f'(500).
c. Determine a rule for f'.

Answer & Explanation

Lillianna Mendoza

Lillianna Mendoza

Beginner2022-07-31Added 16 answers

Step 1
Since Julia drove at constant speed
a) Time and distance follow a linear relation.
given at time t = 1 / 2 distance f = 155 miles and at t = 2 h x   f = 260 miles
i.e. two points on line are ( 1 2 , 155 ) and (2,260)
By two point form, equation of line is
( f 155 ) = 260 155 2 1 / 2 ( t 1 2 )
f 155 = 105 × 2 3 ( 2 t 1 2 )
f 155 = 35 ( 2 t 1 )
f = 70 t + 120 ( 1 )
Step 2
c) f = 70 (By differentiating (1))
f ( t ) = 70 t
Step 3
b ) f ( 500 ) = 70 which is constant speed i.e. 70 miles/hr of Julia

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