A person decides to invest

​$11001100

of his 401K funds into an account that pays

5.85.8​%

interest compounded continuously. The table contains input and output values that represent the amount an initial investment of

​$11001100

is worth at the end of each year.

Year

1

2

3

4

5

Total investment​ (in $)

1166

1235

1309

1387

1470

Does the table contain data that represent a linear​ function?

To determine if the data in the table represents a linear function, we need to check if the values in the table increase by a constant amount each year. In a linear function, the change in the output (total investment) over equal intervals of the input (years) must be constant.

### Given dataTo determine if the data in the table represents a linear function, we need to check if the values in the table increase by a constant amount each year. In a linear function, the change in the output (total investment) over equal intervals of the input (years) must be constant.

### Given 
| Year | Total Investment ($) |
|------|-----------------------|
| 1    | 1166                  |
| 2    | 1235                  |
| 3    | 1309                  |
| 4    | 1387                  |
| 5    | 1470                  |

Now, calculate the difference between consecutive years to see if the increase in the investment is constant:

- From year 1 to year 2: $ 1235 - 1166 = 69 $
- From year 2 to year 3: $ 1309 - 1235 = 74 $
- From year 3 to year 4: $ 1387 - 1309 = 78 $
- From year 4 to year 5: $ 1470 - 1387 = 83 $

The increases are not constant, so this is **not** a linear function. The values grow by larger amounts as time progresses, which is typical of exponential growth (as expected with continuous compounding of interest).

### Conclusion:
The table does not represent a linear function because the differences between consecutive values are not constant. Instead, it suggests an exponential growth pattern due to the continuous compounding of interest.

Would you like more details on continuous compounding or how to calculate the future value of the investment?

### Related Questions:
1. How do you calculate continuous compounding interest?
2. What is the formula for exponential growth in financial investments?
3. How would the investment value change if the interest rate were different?
4. Can you explain the difference between simple and compound interest?
5. How would the investment behave over 10 or 20 years with continuous compounding?

**Tip:** In continuous compounding, the formula for future value is $ A = P e^{rt} $, where $ P $ is the principal, $ r $ is the interest rate, and $ t $ is time.

A person decides to invest $1100 of his 401K funds into an account that pays 5.8% interest compounded continuously. The table contains input and output values that represent the amount an initial investment of $1100 is worth at the end of each year. Does the table contain data that represent a linear function?

Explore whether an investment of $1100 at 5.8% interest compounded continuously grows linearly or exponentially. Analyze a table of values for each year and learn how continuous compounding affects investment growth over time. Suitable for high school students in Grades 10-12.

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