Question

A new car worth ​$26000 is depreciating in value by ​$2000 per year. Complete parts​ (a) through​ (c). a. Write a formula that models the​ car's value,​ y, in​ dollars, after x years. b. Use the formula from part​ (a) to determine after how many years the​ car's value will be ​$16000. c. Graph the formula from part​ (a) in the first quadrant of a rectangular coordinate system.​

Answer 1

The formula that models the car's value is y = 26,000 - 2,000x. After 5 years, the car's value will be $16,000. To graph the formula, plot points for different values of x and y.

Step-by-step explanation:

a. To write a formula that models the car's value after x years, we start with the initial value of $26,000 and subtract $2,000 for each year. The formula is y = 26,000 - 2,000x.

b. To determine after how many years the car's value will be $16,000, we substitute y = 16,000 into the formula from part (a) and solve for x. We have the equation 16,000 = 26,000 - 2,000x. By rearranging the equation, we find that x = 5. So, after 5 years, the car's value will be $16,000.

c. To graph the formula from part (a) in the first quadrant of a rectangular coordinate system, we plot points for different values of x and y. We can start with x = 0 and find the corresponding y-value by substituting x = 0 into the formula. This gives us y = 26,000 - 2,000(0) = 26,000. So, the first point is (0, 26,000). We can repeat this process for other values of x to get more points, and then connect them to create the graph.