College algebra word problem

Question

A car purchased for $35,890 is expected to depreciate according to the formula
f(x) = −1940x + 35,890,
where
f(x)
is the value of the car after x years. After how many years will the car be worthless?

 

I would also appreaciate if you could show me how you worked the problem. Please and thank you.

Answer 1

If f(x) is the value of the car after x years then if the car were worthless (or it had $0 value)

then set f(x) = 0 and solve for x years.

 

f(x) = 0 = -1940*x + 35, 890

 

or

 

1940*x = 35,890

 

x = 35,890/1940 = 18.5 years after purchase

Answer 2

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up an algebraic expression that represents the information given in the question. On this one we have

x = 35890 / 1940 because you want to take the starting value and then divide by the per year decrease to figure out how long it will take for the value to decline down to 0

when I do that calculation on this one I get

x = 35890 / 1940 = 18.5, meaning that the car will be worthless after 18.5 years

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)