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

Answer:

The sequence is a function

Step-by-step 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.