Question

Time (years) 1 2 3 4 5 Account Balance ($) 4,421 4,750 5,262 5,900 6,500 Gene oversees a stock portfolio account for his company. Gene was told by his boss that if the account is not projected to reach $10,000 within the next 5 years, the stocks need to be sold immediately. To make the best decision, Gene compiled the account balances from the last 5 years and constructed the rounded regression equation model y=3,951.33(1.10)x . Calculate the account balance at 10 years and decide if Gene should sell or maintain the stock portfolio account. Decision #1: Gene should sell the stocks as the account balance will not reach $10,000 within the next 5 years. Decision #2: Gene should maintain the account as the balance will exceed $10,000 within the next 5 years. (1 point) Gene should choose Decision #

Answer 1

To determine whether Gene should sell or maintain the stock portfolio account, we need to calculate the account balance at 10 years using the provided exponential growth model, which is given by the equation:

\[ y = 3,951.33(1.10)^x \]

Here, \( x \) represents the number of years. We substitute \( x = 10 \) into the equation to calculate the account balance at 10 years:

\[
y = 3,951.33(1.10)^{10}
\]

Calculating \( (1.10)^{10} \):

\[
(1.10)^{10} \approx 2.59374 \quad (\text{rounded to five decimal places})
\]

Now substituting this value back into the equation:

\[
y = 3,951.33 \times 2.59374 \approx 10,248.48
\]

So, the projected account balance at 10 years is approximately **$10,248.48**.

Since this amount exceeds $10,000, Gene should maintain the stock portfolio account.

Thus, the decision is:

**Gene should choose Decision #2: Gene should maintain the account as the balance will exceed $10,000 within the next 5 years.**