Final answer:
To determine the gallons of oil used when the average monthly temperature is 70 degrees Fahrenheit, the given function A(t) = -1.4t + 96 is used, resulting in A(70) = -2, which suggests no oil is used at that temperature or the model doesn't apply.
Step-by-step explanation:
The student has been given a linear function A(t) = -1.4t + 96 which best fits the data representing the relationship between the gallons of oil used to heat a house and the average monthly temperature, measured in Fahrenheit, over a period of 5 months. To find the value of A(70), which represents the gallons of oil used when the average temperature is 70 degrees Fahrenheit, we simply substitute t = 70 into the function.
So, A(70) = -1.4(70) + 96 = -98 + 96 = -2.
However, because it does not make sense to use negative gallons of oil, this result may indicate that there are no gallons used at 70 degrees Fahrenheit or that the linear model does not apply at this temperature. It's important to consider the context and the feasible range of the data when interpreting this result.