A laptop computer is purchased for $1400 . Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $200 or less?

Answer 1

1400(0.75)^t≤ 200

0.75^t ≤ 1/7

ln(0.75^t) ≤ ln(1/7)

tln(0.75) ≤ ln(1/7)

t ≥ ln(1/7)/ln(0.75)

t ≥ 6.76

Why did the sign switch? The natural log of a number between 0 and 1 is negative, and dividing by a negative switches the sign.

So, after 7 years, the laptop computer will be worth $200 or less.