Chapter 6.1, Problem 39E

To determine

To describeand correct the error in writing a model for the value of the stock.

Answer to Problem 39E

Theformula of compound interest in written model for the value of the value is incorrect and the correct model is $y=500{(1-0.02)}^t$

Explanation of Solution

Given information :

  $\$500$ deposited in the stock of a companyand the value of stock decrease 2% each year

Calculation :

With decrease rate per year (1 times per year), the balance after $t$ year is

  $\begin{array}{l}y=\left(\begin{array}{l}\text{initial}\\ \text{amount}\end{array}\right){\left(1-\text{decay factor}\right)}^t\\ y=500{\left(1-0.02\right)}^t\end{array}$

Hence, theformula of compound interest in written model for the value of the value is incorrect and the correct model is $y=500{(1-0.02)}^t$ .