You buy a used car for 6599. its value decreases by 12% every year.

a. write a function that represents the value y(in dollars) of the car after t years

b. what will cars value be after 2.5 years?

c. what is the value of the car after 20 years?

d. when will the cars value be $2000?

c. when will the cars value be 0?

For a, the starting value (intercept) is 6599. The depreciation rate 12%/year. This is where the function y = 6599(1-(rate)^t) comes into play. 6599 is the starting price, rate is the 12%, and t is the time in years. So the equation is: y = 6599(0.88)^t. For part b, simply plug 2.5 in for t which results in $4,794. For part c, same deal, plug in 20 for t, which results in $512. For part d, you have to take the anti-log where 2000 = 6599(0.88)^t... divide both sides by 6599... 2000/6599 = (0.88)^t. Which is approximately 8.5 years.

This equation is written in point-slope form (y-y1)=m(x-x2). Since the variable m always represents slope in basic mathematics then the slope is 5.