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Answer:
[tex]f(x)=200\cdot(0.85)^x[/tex]
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:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
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:
[tex]f(x)=200\cdot(1-0.15)^x[/tex]
Operating, the function is:
[tex]\mathbf{f(x)=200\cdot(0.85)^x}[/tex]
The function to represent the wave of the skateboard f (x) in dollars after I years since buying it is[tex]200 \times (85)^x[/tex]
[tex]= 200 \times (1- 0.15)^x\\\\= 200 \times (0.85)^x[/tex]
Based on the above information, the same equation should be considered.
learn more about the function here: https://brainly.com/question/11364456