Question

At the beginning of an experiment, there are 400 grams of contaminants. Each hour, three-fourths of the contaminants are filtered out.
A. Formulate a recursive sequence modeling the number of grams after n hours.
B. Use the model to calculate the amount of contaminants after the third hour of the experiment.

Answer 1

We have that

A).Formulate a recursive sequence modeling the number of grams after n hours.
a(n) = 0.75*a(n-1)

B) .Use the model to calculate the amount of contaminants after the third hour of the experiment. 
 for the first hour
a(1) = 0.75*a(0)
a0=400 g
 a1=(3/4)400 = 300 g

for the second hour
a(2) = 0.75*a(1)
a1=300 g
a2=(3/4)300 = 900/4 g

for the third hour
a(3) = 0.75*a(2)
a2=900/4 g
(3/4)900/4 = 2700/16 = 168.75 g

 the answer is 168.75 g

Answer 2

Answer:

18.75g

Step-by-step explanation:

The reason this is right and not the other answer is because you are supposed to multiply by 0.25 not 0.75. When you multiply by 0.75 you get how much of the contaminants are gone. Not how much is still left.

You can use the same equation as above, but you will need to plug in 0.25 where 0.75 is. I'm working on this problem and got it wrong and my teacher said that was my only mistake. :))