Question

A cell phone costs $750 and loses 28% of its value each year. Write an exponential decay function to represent this situation.

1. f(x)= 750 • 0.72^x
2. f(x)= 0.72 • 750^x
3. f(x)= 750 • 0.28^x
4. f(x)= 0.28 • 750^x

Answer 1

1.
`f(x) = 750\cdot 0.72^(x)`

Explanation:

The cell phone experiments an exponential depreciation, which is defined by the following formula:

`f(x) = C_(o)\cdot (1-r)^(x)`, for
`0<r< 1`. (1)

Where:

`C_(o)` - Initial cost, measured in monetary units.

`r` - Depreciation rate, no unit.

`x` - Time, measured in years.

`f(x)` - Current value of the cell phone, measured in monetary units.

If we know that
`C_(o) = \$\,750` and
`r = 0.28`, then the exponential decay function that represents the situation is:

`f(x) = 750\cdot 0.72^(x)`

Which means that correct answer is 1.