Question

Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer.

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Answer 1

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Which option should Belinda choose? Explain your answer, and show the investment value after 20 years for each option.

Answer 2

82,000

Show that the relationship between variables is linear.

Solution:

With Year as the explanatory variable, and Total Votes as the response variable, we check that the slope (rate of change) between successive points is constant.
(78,000 - 74,000) / (1972 - 1968) = 4,000 / 4 = 1,000 votes per year
(82,000 - 78,000) / (1976 - 1972) = 4,000 / 4 = 1,000 votes per year

In some cases, values which grow (or decay) do not do so linearly, but exponentially.



Example 6.3:
End of Month

Amount of Debt
0 $500.00
1 $550.00
2 $605.00
3 $665.00
4 $732.05

With Month as the explanatory variable, and Debt as the response, it is easy to see that the relationship between the variables is not linear. The rate of change between successive points is not constant, but there is a relationship between the data.

Let's look at the ratios of the current month's debt to the previous month's debt, for successive points.
550 / 500 = 1.1
605 / 550 = 1.1
665 / 605 = 1.1
732.50 / 665 = 1.1

Since the ratios are constant, we can represent the amount of debt as a function:
Debt = 500 * (1.1month)

This is an exponential function since the explanatory variable is in the exponent of a constant.

If we write our constant as 1 + 0.10, we can see that the debt is growing at 10% per month.

If the constant in the exponential is less than 1, it would show exponential decrease (or decay). For instance, a function representing a 10% decrease would have a constant of 1 - 0.10 = 0.90, giving a function such as:
Debt = 500 * (0.90month)

Answer 3

For Part A, have you tried getting the functions? The first option seems to define a linear function since there is an interval of 300 between every two values of the amount.

Answer 4

@navk sorry i wasn't able to write back the website wouldn't let me back in.

Answer 5

@meilendurcer so did you try to identify the functions in the table? What did you get?