The discounts State Farm offers to customers who have insured a vehicle with the company are shown in Table 58 for various years of loyalty.
Let p be the discount (in percent) for customers who have insured a vehicle with the company for t years.
a. Construct a scatterplot by hand, and draw a linear model on the scatterplot.
b. Use the model to predict the number of years of loyalty it takes to reach a 6% discount.
c. A customer’s car has been insured by State Farm for 5 years. Without the loyalty discount, the customer would have to pay $120 per month. Use the model to predict how much money the customer actually has to pay per month.
d. It turns out that a linear model does in fact predict the correct discount for every year of loyalty up to 6 years. Up until now, State Farm used to offer no discount for up to 2 years of loyalty, a 10% discount for 3 to 5 years of loyalty, and an 18% discount for at least 6 years of loyalty. For which years of loyalty is the new policy the bet- ter deal?
e. A customer’s car has been insured by State Farm for 6 years. Without any loyalty discounts, the customer would have had to pay $100 per month for the past 6 years. Find the total amount of money the customer would have saved if the new policy had been in effect rather than the old policy.