A car with a cost of $25,000 is decreasing in value at a rate of 10% each year. The function g(t)= 25,000(0.9)^t gives the value of the car after t years. When will the value of the car be about $12,000? A) after 7 years B) after 9 years C) after 13 years
Could you also explain how to do it?
12,000 = 25,000 [tex] (0.9)^{t} [/tex] Divide both sides by 25,000 → 0.48 = [tex] (0.9)^{t} [/tex] Convert to log form → [tex] log_{0.9} [/tex] 0.48 = t Use the change of base formula → [tex] \frac{log 0.48}{log 0.9} [/tex] = t Plug into the calculator → 6.966 = t
