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Answer :
Sure! Let's break down the problem and solve it step-by-step.
a) Writing a function rule for the total bill [tex]\( b \)[/tex] as a function of the days [tex]\( d \)[/tex] the car is rented:
1. Cost per day for renting the car: The car costs \[tex]$29 per day.
2. Cost per day for renting the GPS: The GPS costs \$[/tex]11.95 per day.
3. Cost for a full tank of gas: The cost per gallon is \[tex]$4.30, and since the tank is 14 gallons, the cost for a full tank is calculated as follows:
\[
4.30 \times 14 = 60.20 \, \text{(approximately)}
\]
4. Function Rule:
The total daily cost for both renting the car and GPS is:
\[
29 + 11.95 = 40.95 \, \text{per day}
\]
The total bill \( b \) for \( d \) days, including a single full tank of gas, would be:
\[
b = 40.95d + 60.20
\]
So, the correct function rule is \( b = 40.95d + 60.20 \).
b) Calculating the bill for a 5-day rental:
1. Using the function rule:
Substitute \( d = 5 \) into the function:
\[
b = 40.95 \times 5 + 60.20
\]
2. Calculate the total:
\[
40.95 \times 5 = 204.75
\]
Adding the gas cost:
\[
204.75 + 60.20 = 264.95
\]
Thus, the total bill for a 5-day rental is \$[/tex]264.95.
Therefore, the correct answer is option C: [tex]\( b = 40.95d + 60.20 \)[/tex]. For a 5-day rental, the bill amounts to \$264.95.
a) Writing a function rule for the total bill [tex]\( b \)[/tex] as a function of the days [tex]\( d \)[/tex] the car is rented:
1. Cost per day for renting the car: The car costs \[tex]$29 per day.
2. Cost per day for renting the GPS: The GPS costs \$[/tex]11.95 per day.
3. Cost for a full tank of gas: The cost per gallon is \[tex]$4.30, and since the tank is 14 gallons, the cost for a full tank is calculated as follows:
\[
4.30 \times 14 = 60.20 \, \text{(approximately)}
\]
4. Function Rule:
The total daily cost for both renting the car and GPS is:
\[
29 + 11.95 = 40.95 \, \text{per day}
\]
The total bill \( b \) for \( d \) days, including a single full tank of gas, would be:
\[
b = 40.95d + 60.20
\]
So, the correct function rule is \( b = 40.95d + 60.20 \).
b) Calculating the bill for a 5-day rental:
1. Using the function rule:
Substitute \( d = 5 \) into the function:
\[
b = 40.95 \times 5 + 60.20
\]
2. Calculate the total:
\[
40.95 \times 5 = 204.75
\]
Adding the gas cost:
\[
204.75 + 60.20 = 264.95
\]
Thus, the total bill for a 5-day rental is \$[/tex]264.95.
Therefore, the correct answer is option C: [tex]\( b = 40.95d + 60.20 \)[/tex]. For a 5-day rental, the bill amounts to \$264.95.
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