For a car travelling at a constant speed of 80km/h, the distance driven, d kilomtres, is represented by d(t)= 50t, where t is the time in hours. The cost of gasoline, in dollars, for the drive is represented by C(d)= 0.07d.
a)Determine C(d(8)) numerically and interpret your result.
b)Describe the relationship represented by C(d(t)).
d(8) = 50*8 = 400 km
C(400) = .07 * 400 = $ 28
or C (t) = .07 * 50 * t = 3.5 t
Thank you
a) To determine C(d(8)), we need to substitute the value of t = 8 into the function d(t) first.
d(t) = 50t
d(8) = 50 * 8
d(8) = 400 kilometers
Now, we can substitute the value of d(8) into the function C(d).
C(d) = 0.07d
C(d(8)) = 0.07 * d(8)
C(d(8)) = 0.07 * 400
C(d(8)) = 28 dollars
Interpretation: C(d(8)) represents the cost of gasoline for a car that has driven a distance of 400 kilometers (which took 8 hours) at a constant speed of 80 km/h. The cost of gasoline for this drive is 28 dollars.
b) The relationship represented by C(d(t)) is the cost of gasoline (in dollars) as a function of the distance driven (in kilometers) at a constant speed of 80 km/h. The function is linear, with a rate of change of 0.07 dollars per kilometer. This means that for every kilometer driven, the cost of gasoline increases by 0.07 dollars.
To determine C(d(8)) numerically, we need to substitute d = 50t into the function C(d).
C(d(8)) = C(50 * 8)
C(d(8)) = C(400)
Now, substitute 400 into the function C(d) to find the cost:
C(d) = 0.07d
C(400) = 0.07 * 400
C(400) = $28
a) Therefore, C(d(8)) is equal to $28. This means that the cost of gasoline for a car that traveled a distance of 400 kilometers (d(8) = 50 * 8 = 400) at a constant speed of 80 km/h will be $28.
b) The relationship represented by C(d(t)) is a linear relationship, where the cost of gasoline is directly proportional to the distance traveled. As the distance driven increases, the cost of gasoline increases proportionally. In this case, the cost per kilometer is $0.07.