In a chemical reaction, a compound X is formed from two compounds Y and Z. The masses in grams of X, Y and Z present at time t seconds after the start of the reaction are x, 10 – x and 20 – x respectively. At any time the rate of formation of X is proportional to the product of the masses of Y and Z present at the time. When t = 0, x = 0 and\(\frac{dx}{dt}\) = 2.
\(\frac{dx}{dt}=0.01(10-x)(20-x)\)
Find an expression of x in terms of t
(I.e. x(t)=...)
