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Jessica's car gets 18 miles per gallon w...

Jessica's car gets 18 miles per gallon when the car travels at an average speed of 35 miles per hour. Jessica begins a trip with 14 gallons of gas, and she travels at 35 miles per hour for the first 4 hours of her trip. Which of the following functions g is the most accurate model for the number of gallons of gallons of gas remaining in the tank t hours after the trip begins for `0le t le4`?

A

`g(t)=(14-35t)/(18)`

B

`g(t)=(14-18t)/(35)`

C

`g(t)=14-(35t)/(18)`

D

`g(t)=14-(18)/(35t)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find a function \( g(t) \) that represents the number of gallons of gas remaining in Jessica's car after \( t \) hours of travel. Here's a step-by-step breakdown of the solution: ### Step 1: Identify Initial Conditions Jessica starts her trip with 14 gallons of gas. ### Step 2: Determine the Distance Traveled Jessica travels at an average speed of 35 miles per hour. Therefore, the distance she travels in \( t \) hours is given by: \[ \text{Distance} = \text{Speed} \times \text{Time} = 35 \times t \text{ miles} \] ### Step 3: Calculate Gas Consumption Jessica's car consumes gas at a rate of 18 miles per gallon. This means for every 18 miles, she uses 1 gallon of gas. To find out how much gas is used for the distance traveled in \( t \) hours, we can set up the following relationship: \[ \text{Gas used} = \frac{\text{Distance}}{\text{Miles per gallon}} = \frac{35t}{18} \text{ gallons} \] ### Step 4: Determine Remaining Gas To find the remaining amount of gas after \( t \) hours, we subtract the gas used from the initial amount of gas: \[ \text{Remaining gas} = \text{Initial gas} - \text{Gas used} = 14 - \frac{35t}{18} \] ### Step 5: Define the Function We can express the remaining gas as a function of time \( t \): \[ g(t) = 14 - \frac{35t}{18} \] ### Step 6: Verify the Function Now we need to check if this function is consistent with the options provided. The function we derived matches option 3: \[ g(t) = 14 - \frac{35t}{18} \] ### Conclusion Thus, the most accurate model for the number of gallons of gas remaining in the tank \( t \) hours after the trip begins is: \[ g(t) = 14 - \frac{35t}{18} \]
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