Question

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. How do you write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years?

Answer 1

`y=3500*e^(k*9.5)`

Explanation:

Exponential equations can be written simply like this:
`y=A*e^(kt)`

whereby:
`y`: value
`A`: constant;
`k`: rate of change
`t`: time since the start

In this case,
`3500=A*e^(k*0)`
`3500=A`

Hence, after 9.5 years, the value of the boat is:
`y=3500*e^(k*9.5)`

`k`, the yearly depreciation rate in this case, still being unknown and have to be derived or determined by you. Also, since it is depreciation rate, `k` is a negative value.