Rational Expressions and Equations math problem

Question

A large mixing tank currently contains 110 gallons of water into which 5 pounds of sugar have been mixed. A tap will open pouring 25 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 2 pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after 14 minutes. Is that a greater concentration than at the beginning?

Write a function that models this:

 

C(t)=

 

what will the concentration be in 14 minute's?

C(14)=

Answer 1

You are given that initially, at t=0, the concentration is 5 pounds of sugar per 110 gallons of water or c(0)=5/110=1/22~.045 pounds of sugar per gallon of water. Since sugar is being added at a rate of 2 pounds per minute and water is being added at a rate of 25 gallons per minute, the concentration (pounds of sugar per gallon water) at some minute t, is c(t)=(1+2t)/(22+25t). The concentration after 14 minutes has passed, c(14)=29/372~.078 pounds of sugar per gallon. The concentration has increased.