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

1. Let $a_{i}$ be the amount of the limonade in the container.

2. 

$a_{1} =64$


$a_{2} =(64-16)+ \frac{25}{100}(64-16)=(64-16)(1+0.25)=1.25*48$




3. To find each $a_{n}$, the procedure is as in step 2, that is :

$a_{n} =(a_{n-1}-16)+ \frac{25}{100}(a_{n-1}-16) =(a_{n-1}-16)(1+0.25) =1.25*(a_{n-1}-16)$

4. Thus the right choice is A.