If the rate of decay is 6% per year, that means the motorcycle retains 93% of its value every year. Because there are 12 months in a year, you can use the following equation: x^12 = 0.94, where x = the rate of decay each month, 12 = the number of months, and 0.94 = the retained value each year. Next, set a logarithmic function on each side as such: LOG(x^12) = LOG(0.94) When applying log functions, exponentials (like the 12 in the equation) are moved outside of the function like so: LOG(x^12) = 12(LOG(x)) Therefore, 12(LOG(x)) = LOG(0.94) = -0.0268721464 When you divide both sides by 12, the equation becomes LOG(x) = -0.00223934553 Finally, remove the LOG from the left side by applying both sides of the each by 10^() as such: 10^(LOG(X)) = 10^(-0.00223934553) X = 0.994856987 Therefore, the motorcycle retains that 0.994856987 of its value every year. 1 - 0.994856987 = 0.005143 Expressed as a percentage, this value is 0.5143013%
