Algebra 1 Math Question

Question

You buy a used car for $6599.Its value decreases by 12% each year.

-When(how many years) will the value be 0?

Answer 1

Never. It will approach zero, but never reach zero. It will get closer & closer to zero, but always have some positive value. that's true whether it's 12% or anything less than 100%. It will reach numbers so close to zero it makes no practical difference, but still never reach zero.

Answer 2

0 = 6599(0.88)^t

Note: This equation cannot be solve. The product of positive numbers is always positive, greater than zero. The problem is incorrectly posed.

Now, if

0.01 = 6599(0.88)^t

0.000001515 ≈ 0.88^t

ln 0.000001515 ≈ ln 0.88 t

-13.3998 ≈ -0.1278 t

104.8 ≈ t

The car shall be worth approximately one cent after 105 years.