Calculate the Rate of Change?

Question

A lake has a volume of 10^8 m^3. A river flows into the lake at the rate of 2 \times 10^5 m^3/day. The same amount of pure water evaporates from the lake each day, so the volume of the lake does not change. The river contains 7\% pollution. The lake is initially unpolluted.

(a) What is the percentage pollution in the lake after t days?

(b) When does the pollution in the lake reach 1\%?

Answer 1

(a)

P/100 = (7/100)(2*10^5 m^3/da)t/(10^8 m^3)

P = 0.014%t, t in days

(b)

t = 1%/0.014%

t ≈ 71.429 days ≈ 71.4 days