• James invested three dollars in the Junior Stock Market on day one. The money was doubled each day for seven days. Show on a table the value of the money that was doubled for each day and write each day’s amount in exponential form.
• How much money did he save over the seven-day period?
 

### Table of the Doubling Investment in Exponential Form

James invested $3 on the first day, and his money doubled each day for seven days. The exponential form to represent the value of his investment on each day is given by:

\[
\text{Day's amount} = 3 \times 2^n \quad \text{where} \ n \ \text{is the day number (starting from 0)}
\]

Here’s a table showing the value for each day:

| **Day** | **Exponential Form**         | **Amount (in dollars)**    |
|:-------:|:-----------------------------|:--------------------------|
| Day 1   | $ 3 \times 2^0 $            | 3                         |
| Day 2   | $ 3 \times 2^1 $            | 6                         |
| Day 3   | $ 3 \times 2^2 $            | 12                        |
| Day 4   | $ 3 \times 2^3 $            | 24                        |
| Day 5   | $ 3 \times 2^4 $            | 48                        |
| Day 6   | $ 3 \times 2^5 $            | 96                        |
| Day 7   | $ 3 \times 2^6 $            | 192                       |
| Day 8   | $ 3 \times 2^7 $            | 384                       |

### Total Money Saved Over 7 Days
To find the total money saved, sum up all the amounts from each day:

\[
3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 = 765 \ \text{dollars}
\]

### Final Answer
James saved a total of **765 dollars** over the seven-day period.

Would you like more details on any part of the calculation, or do you have any questions?

### 5 Related Questions:
1. What is the general formula to compute total savings for any investment that doubles each day for $n$ days?
2. How much would James have saved if he started with $5 instead of $3 and doubled for seven days?
3. What would the total amount be if his money doubled every other day instead of every day?
4. How would the growth pattern change if James only added a fixed amount instead of doubling?
5. What is the importance of exponential growth in financial investments?

**Tip:** Exponential growth occurs when a quantity increases by a consistent factor over equal intervals, a crucial concept in finance and biology.

James invested three dollars in the Junior Stock Market on day one. The money was doubled each day for seven days. Show on a table the value of the money that was doubled for each day and write each day’s amount in exponential form. How much money did he save over the seven-day period?

Explore how James's $3 investment doubled each day for 7 days, reaching $384 by day 7. This table includes exponential expressions for each day, as well as the total saved amount of $765. Perfect for students learning about exponential growth and arithmetic series, ideal for Grades 5-7.

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