Question

Write a function in terms of t that represents the situation. A company profit of $20,000 decreases by 13.4% each year

Answer 1

The profit function is .https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et

Step-by-step explanation:

The exponential decay function is defined as

https://tex.z-dn.net/?f=P%28t%29%3Da_0%281-r%29%5Et

Where, a₀ is initial value, r is rate of change and t is time (in year).

From the given information it is noticed that the initial profit is $20,000 and it decreases by 13.4% each year.

The profit function is defined as

https://tex.z-dn.net/?f=P%28t%29%3D20000%281-%5Cfrac%7B13.4%7D%7B100%7D%29%5Et

https://tex.z-dn.net/?f=P%28t%29%3D20000%281-0.134%29%5Et

https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et

Therefore the profit function is .

https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et