Chapter 6.2, Problem 30E

To determine

To find:the function that represent the situation given.

Answer to Problem 30E

The function representing the given situation is $\boxed{y=20000{\left(0.866\right)}^t}$

Explanation of Solution

Given information:A company profit of $20,000 decreases by 13.4% each year.

Concept Involved:

Exponential decay function is given by $A=A_0{\left(1-r\right)}^t$ where $A_0$ is the initial amount, r is the rate of decay and t is the time {here year}.

Calculation:

Substitute the given information $A_0=20000,$

  $r=13.4\%$ in exponential decay function

  $A=20000{\left(1-13.4\%\right)}^t$

Rewrite the 9.5% as decimal

  $A=20000{\left(1-0.134\right)}^t$

Simplify as much as possible inside the parenthesis

  $A=20000{\left(0.866\right)}^t$