Question

Jill has 64 ounces of lemonade. Each day, her brother drinks 16 ounces. Then at the end of each day Jill adds 25% of the remaining total back into the lemonade container. Which recursive formula models the amount of lemonade in the container, an?
A, B, C AND D goes from left to right

Answer 1

Answer: $a_n= 1.25( a_{n-1} - 16)$

Step-by-step explanation:

Let initially the total quantity of the drink = $a_{n-1}$

Then after 1 day the quantity of the drink = $a_{n}$

Since, according to the question,

Each day, her brother drinks 16 ounces. Then at the end of each day Jill adds 25% of the remaining total back into the lemonade container.

That is, $a_n= (a_{n-1}-16)+ 25% of (a_{n-1}-16)[\tex] =

[tex]a_n= (a_{n-1}-16)+ \frac{25}{100}\times (a_{n-1}-16)$

⇒ $a_n= (a_{n-1}-16)+ 0.25\times (a_{n-1}-16)$

⇒  $a_n= a_{n-1}-16+ 0.25 a_{n-1}-0.25\times 16$

⇒  $a_n= 1.25 a_{n-1}-0.25\times 16-16$

⇒ $a_n= 1.25 a_{n-1}-20$

⇒ $a_n= 1.25( a_{n-1} - 16)$ where $a_1 = 64$

Which is the required recursive formula.

Thus, Option first correct.

Answer 2

The value of $\rm a_n$ is 64. The first option is correct.

What are the ratio and proportion?

A ratio is an ordered couple of numbers a and b, shown as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

Jill has 64 ounces of lemonade. Each day, her brother drinks 16 ounces. Then at the end of each day, Jill adds 25% of the remaining total back into the lemonade container.

To find

Which recursive formula models the amount of lemonade in the container.

How to get the equation?

Let, initially the total quantity drink = $\rm a_{n-1}$

After one day the quantity drink = $\rm a_n$

According to the condition, the equation will be

$\rm a_n = (a_{n-1} - 16) + 25\\\\\rm a_n = (a_{n-1} - 16) + 0.25 (a_{n-1} - 16) \\\\\rm a_n = 1.25a_{n-1} - 20\\\\\rm a_n = 1.25(a_{n-1} - 16)$

Here $\rm a_1$ = 64

Thus, the first option is correct.

More about the ratio and proportion link is given below.

https://brainly.com/question/165414