Question

Kyle starts saving for his first car by opening a savings account and depositing $100 . He plans to make a deposit every month to continue saving. The amount of money in Kyle's savings account can be modeled by the sequence 0=100, , =−1+75 , where is the number of months since his initial deposit. Is the sequence a function? Why or why not?

Answer 1

Yes, because for each input value, n, there is only one possible output value.

Explanation:

Answer 2

The sequence is a function

Explanation:

Given

Sequence:
`A_0=100`;
`A_n=A_(n-1)+75`

Required

Is the sequence a function

To determine if the sequence is a function or not, we start by calculating its range from the domain:

When n = 0;
`A_0=100`

When n = 1:
`A_1 = A_(1-1) + 75 = A_0 + 75 = 100 + 75 = 175`

When n = 2;
`A_2 = A_(2-1) + 75 = A_1 + 75 = 175 + 75 = 250`

When n = 3;
`A_3 = A_(3-1) + 75 = A_2 + 75 = 250 + 75 = 325`

This implies that:

The domain (n) and the range (An) can be represented as:

`\left[\begin{array}{c}n&-&0&1&2&3\\-&-&-&\end{array}\right]`
`\left[\begin{array}{c}A_n&-&100&175&250&325\\-&-&-&\end{array}\right]`

The above shows that the sequence is a one to one relation and a one to one relation is always a function.