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

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.