Final answer:
The rate of change of the gasoline in the tank at t = 3.5 is found by differentiating the function G(t) = 18e^t, which results in G'(t) = 18e^t. Substituting t with 3.5 into the derivative gives us the rate, with the correct answer being 8.938 gallons per hour.
Step-by-step explanation:
The student is asking about the rate of change of the amount of gasoline in a car's tank at a specific time, which is a calculus problem involving the derivative of an exponential function. The function representing the amount of gasoline remaining in the tank is G(t) = 18e^t, and we need to find the rate of change at t = 3.5 hours. To find this rate, we must differentiate the function with respect to time (t).
The derivative of G(t) with respect to t is G'(t) = 18e^t because the derivative of e^t with respect to t is e^t, and by the constant multiple rule, we multiply e^t with the constant 18. To find the rate of change at t = 3.5, we simply substitute t with 3.5 in the derivative, yielding G'(3.5) = 18e^(3.5).
Calculating this value gives us the rate of change in gallons per hour, which is the answer the student is seeking. Option (d), 8.938 gallons per hour, is the closest to the calculated value and is therefore the correct answer to the student's question.