Question

Suppose you start with one liter of vinegar and repeatedly remove 0.08 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n n steps.

Answer 1

0.92^n

Step-by-step explanation:

Given that :

Initial amount of vinegar = 1 Litre

Number of litres removed repeatedly = 0.08 Litre

Since the amount removed each time is constant, then ;

Initial % = 100% = 100/100 = 1

. Using the relation :

Amount of vinegar in mixture :

Initial * (1 - amount removed / initial amount)^n

n = number of times repeated

1 * (1 - 0.08/1)^n

1 * (1 - 0.08)^n

1 * 0.92^n

Hence,

For nth removal,

Concentration will be :

0.92^n ; for n ≥ 1