Question

the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Answer 1

The pattern in the given series of amount in the account are in the form of

arithmetic and geometric progression.

• The function for Option 1 is;  $\underline{ f(n) = 1,100 + (n - 1) \cdot 100}$

• The function for Option 2 is; $\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}$

Reasons:

The given table of values is presented as follows;

$\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right]$

In Option 1, the amount in dollars for each year has a common difference of d = 100

The first term, a = 1,100

Therefore;

The Option 1 can be represented as an arithmetic progression , A.P. in the

form, tₙ = a + (n - 1)·d as follows;

For the Option 1, we have;

• The amount in dollars after n years, $\underline{ f(n) = 1,100 + (n - 1) \cdot 100}$

For Option 2, it is possible to find;

1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1

Therefore;

The terms in the Option 2 have a common ratio of r = 1.1

The Option 2 is a geometric progression, G.P.

The first term in Option 2 is a = 1,100

Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾

Therefor;

• The function for the Option 2 is; $\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}$

Learn more about arithmetic and geometric progression here:

brainly.com/question/8932895

brainly.com/question/22977503