A $17,000 motorcycle depreciates at a rate of 5% each year. Write an exponential function to model this situation.
if it decreases by r% per year, then if the starting value is v0,
v(y) = v0 * (1-r/100)^y
see the two problems below this one, posted under other names ...
17 000 (1 - 0.05)^y
To write an exponential function that models the depreciation of the motorcycle, we can use the general form of an exponential function:
y = a * (1 - r)^x
Where:
- y represents the value of the motorcycle after x years.
- a represents the initial value of the motorcycle, which is $17,000 in this case.
- r represents the depreciation rate per year, which is 5% or 0.05 as a decimal.
Substituting these values into the equation, we have:
y = 17,000 * (1 - 0.05)^x
Simplifying further, we have:
y = 17,000 * (0.95)^x
Therefore, the exponential function that models the depreciation of the motorcycle is y = 17,000 * (0.95)^x.