Question

a motorcycle can be purchased for $9100 or leased for a down payment of $500 and $260 per month. find a function that describes how the cost of the lease depends on time. assuming that the monthly payments are made, how long can the motorcycle be leased before more than the purchase price has been paid?

the function that models the situation is p = , where p is the amount paid on the lease in dollars and t is the time in months.
(simplify your answer.)

Explanation:

Define the linear cost function

Using the Linear Function Modeling knowledge point

$$ p = 260t + 500 $$

Set up the inequality for lease cost vs purchase price

Using the Linear Equations knowledge point

$$ 260t + 500 > 9100 $$

Solve the inequality for time

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Determine the maximum lease duration

Using the Linear Equations knowledge point

$$ t \le 33 $$

Answer:

Question 1

The function that models the situation is \(p =\) <blank>\(260t + 500\)</blank>, where \(p\) is the amount paid on the lease in dollars and \(t\) is the time in months.

Question 2

The motorcycle can be leased for <blank>33</blank> months before more than the purchase price has been paid.