The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the given question. Be sure you clearly identify the independent and dependent variables. Then briefly discuss whether a linear model is reasonable for the situation described The cost of leasing a car is $\$ 900$ for the down payment and processing fee plus $\$ 310$ per month. For how many months can you lease the car with $\$ 3160$ ? Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer. Do not include the \$ symbol in your answer) A. The independent variable is amount paid ( $p$ ), in dollars, and the dependent variable is time $(t)$, in months. The linear function that models this situation is $t=\square$ B. The independent variable is time ( $t)$, in months, and the dependent variable is amount paid $(p)$, in dollars The linear function that models this situation is $p=\square$
Solution
Step 1 ：Identify the independent variable as time $(t)$, in months, and the dependent variable as amount paid $(p)$, in dollars. The linear function that models this situation is $p=310t + 900$.
Step 2 ：This equation represents the total cost of leasing a car for $t$ months. The $310t$ term represents the monthly cost of the lease, and the $900$ represents the initial down payment and processing fee.
Step 3 ：To find out for how many months you can lease the car with $3160, set $p$ equal to $3160$ and solve for $t$.
Step 4 ：Substitute $3160$ into the equation: $3160 = 310t + 900$.
Step 5 ：Subtract $900$ from both sides to get: $2260 = 310t$.
Step 6 ：Divide both sides by $310$ to solve for $t$: $t = \frac{2260}{310} = 7.29$ months.
Step 7 ：Since you can't lease a car for a fraction of a month, round down to the nearest whole number. Therefore, you can lease the car for 7 months with $3160$.
Step 8 ：\(\boxed{7}\) is the final answer.
