Pre- Calculus Hw problem! Please help!

The volume of pollutants, in millions of cubic feet, in a water reservoir at time t, in years, is increasing and is given by P(t)= 350+50t
Total volume of the reservoir including water/pollutants and is also increasing
formula given is V(t)= 12000+120t

The fraction of the reservoir volume that consists of pollutants is then C(t)= P(t)/V(t)

(a) Evaluate and interpret V(0), P(0) and C(0)
b) Evaluate and interpret V(10), P(10), and C(10)
c) After many years, about what percentage of the reservoir's total volume will consist of pollutants? Indicate your reasoning.
d) The reservoir will become unusable when the percentage of pollutants reaches 10%. After how many years will this occur?

a) V(t)= 12000+120t

V(0) = 12000 + 120(0)
V(0) = 12000 + 0
V(0) = 12000

P(t) = 350 + 50t
P(0) = 350 + 50(0)
P(0) = 350 + 0
P(0) = 350

C(t) = P(t)/V(t)
C(0) = P(0)/V(0)
C(0) = 350/12000
C(0) = 35/1200
C(0) = 7/240

When t = 0, that means no time has elapsed and you're looking at the current volume of pollutants P(t), volume of the reservoir V(t), and fraction of the reservoir volume consisting of pollutants C(t).

So right now, the volume of reservoir is 12,000 million cubic feet, or multiplying 12,000 by 1 million... 12 billion cubic feet.

The total volume of the pollutants is 350 million cubic feet.

The fraction of the reservoir volume consisting of pollutants is 7/240. Since it's just a fraction, it won't have units.

b) V(t) = 12000 + 120t
V(10) = 12000 + 120(10)
V(10) = 12000 + 1200
V(10) = 13200

P(t) = 350 + 50t
P(10) = 350 + 50(10)
P(10) = 350 + 500
P(10) = 850

C(t) = P(t)/V(t)
C(10) = 850/13200
C(10) = 85/1320
C(10) = 17/264

When t = 10, you're looking at the volumes after 10 years has passed. So in ten years, the volume of pollutants P(t) is going to be 850 million cubic feet, the volume of the reservoir is going to be (13200 * 1 million) = 13.2 billion cubic feet, and the fraction of the reservoir volume is 17/264.


c) I have no clue what "many years" is so I don't know how to do that.

d) So if a percentage is 10%, we obviously know the fraction is 1/10.

Since C(t) basically tells us what the volume of pollution is over the total volume of the reservoir, setting C(t) = 1/10 is going to tell us how many years (that is, 't') it'll take for the percentage to hit 10%.

C(t) = 1/10
C(t) = P(t)/V(t)
C(t) = [350 + 50t] / [12000 + 120t]
[350 + 50t] / [12000 + 120t] = 1/10

Now cross multiply both sides to get...

[350 + 50t] (10) = (1) [12000 + 120t]

3500 + 500t = 12000 + 120t
3500 + 380t = 12000
380t = 8500
t = 8500/380
t = 22.37 years.

So after 22.37 years, the reservoir becomes unusable.