A moving truck rental company charges $35.95 to rent a truck, plus $0.67 per mile. Suppose the function
C
(
d
)
C(d)
gives the total cost of renting the truck for one day if you drive
d
d
miles.
State the formula for
C
(
d
)
C(d)
. Make sure to give the complete formula as an equation.
C
(
d
)
=
35.95
+
0.67
d
C(d)=35.95+0.67d
syntax ok
Use function notation to give the total rental cost if you drive the truck 74 miles. Give the function notation in the first box, the answer in the second box (rounded to one decimal place), and choose the correct units from the third box.
=
Suppose you have $90 budgeted to move. What is the furthest distance you can drive the truck? Round your answer to the nearest whole number and choose the correct units.
C(d) = 35.95 + 0.67 d
is fine
if d = 74
C = 35.95 + 0.67 * 74
90 = 35.95 + 0.67 d
so
d = (90.00 - 35.95) / 0.67
Here's the answer you're looking for:
Function Notation:
C(74)
Answer:
C(74) = 35.95 + 0.67 * 74 = $81.58
Units:
Dollars ($)
The function notation for the total rental cost if you drive the truck 74 miles is:
C(74)
To find the answer, we substitute 74 for d in the formula C(d):
C(74) = 35.95 + 0.67(74)
Calculating this, we get:
C(74) = 35.95 + 49.58 = 85.53
So the total rental cost for driving the truck 74 miles is $85.53.
For the second question, we have a budget of $90. To find the furthest distance we can drive the truck, we need to solve the equation C(d) = 90.
Substituting the formula for C(d) into the equation and rearranging, we get:
35.95 + 0.67d = 90
Simplifying, we have:
0.67d = 90 - 35.95
0.67d = 54.05
Dividing both sides by 0.67, we find:
d ≈ 80.82
Rounded to the nearest whole number, the furthest distance we can drive the truck is approximately 81 miles.
To find the total rental cost if you drive the truck 74 miles using function notation, you would plug in the value of 74 for "d" in the formula C(d) = 35.95 + 0.67d.
Therefore, the function notation would be:
C(74) = 35.95 + 0.67(74)
To calculate the answer, you would use the formula and solve the equation:
C(74) = 35.95 + 0.67(74)
C(74) = 35.95 + 49.58
C(74) = 85.53
So, the total rental cost is $85.53 (rounded to one decimal place).
Now, to find the furthest distance you can drive the truck with a budget of $90, you can reverse the formula and solve for "d".
Starting with the formula C(d) = 35.95 + 0.67d:
90 = 35.95 + 0.67d
Next, subtract 35.95 from both sides of the equation:
90 - 35.95 = 0.67d
Simplifying further:
54.05 = 0.67d
Lastly, divide both sides of the equation by 0.67 to solve for "d":
d = 54.05 / 0.67
Calculating:
d ≈ 80.82
Rounded to the nearest whole number, the furthest distance you can drive the truck with a $90 budget is 81 miles.