Question

Jim buys a skateboard for $200 The value of the skateboard depreciates by 15% each year since buying it Create

Answer 1

Answer:

$f(x)=200\cdot(0.85)^x$

Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

Depreciation is often modeled as an exponential decay function. Since Jim bought a skateboard for Co=$200, its value will depreciate by r=15% = 0.15 each year since buying it.

The exponential model for this situation is:

$f(x)=200\cdot(1-0.15)^x$

Operating, the function is:

$\mathbf{f(x)=200\cdot(0.85)^x}$