Question

Claire has $300 Is an account. She decides she is going to take out $25 each month.

Answer 1

Recursive equation would be f(x+1) = f(x) - 25 with f(0) = 300

Explicit equation would be f(x) = -25x + 300

And graph would looks like this:

Answer 2

Total amount of Money in Claire account = $300

Amount that,claire is going to take out each month = $ 25

As, she is going to take $25 ,each month ,the money in the account will form an Airthmetic sequence.

Sequence
`S_(n)`

=300+(300-25)+(300-2×25)+(300-3×25)+............+(300-12×25)

=300+275+250+225+200+..................+25+0

First Term =300

Common Difference

=Second term - First term

=275 - 300

= -25

Recursive Formula

`A_(n)=A_(n-1)-25\\\\A_(n)=\text{nth term}\\\\A_(n-1)=\text{(n-1)th term}`

Explicit Formula

`A_(n)=A+(n-1)D\\\\A_(n)=300+(n-1)*25`

Graph will be like this

Y-Intercept=300

If $ 25 is taken out every month,

Number of month required to draw total of $ 300

`=(300)/(25)\\\\=12`

So, equation of line can be derived using point slope form,as line cut x axis at (12,0) and y axis at (0,300).

`\rightarrow (x)/(12)+(y)/(300)=1`