In a chemical reaction a compound X is formed from a compound Y. The masses in grams of X and Y present at time t seconds after the start of the reaction are x and y respectively. The sum of the two masses is equal to 100 grams throughout the reaction. At any time, the rate of formation of X is proportional to the mass of Y at that time. When t = 0, x = 5 and dx/dt = 1.9.

(i) Show that x satisfies the differential equation: dx/dt = 0.02(100 - x).

Question

In a chemical reaction a compound X is formed from a compound Y. The masses in grams of X and Y present at time t seconds after the start of the reaction are x and y respectively. The sum of the two masses is equal to 100 grams throughout the reaction. At any time, the rate of formation of X is proportional to the mass of Y at that time. When t = 0, x = 5 and dx/dt = 1.9.

(i) Show that x satisfies the differential equation: dx/dt = 0.02(100 - x).

unklerhaukus · Answer

$$X+Y = 100$$

$$dX/dt \propto Y\
 \qquad\quad=kY$$

lxelle · Answer

I've got 
dx/dt= k(100-x)
1.9=k(95)
But k isn't 0.02

unklerhaukus · Answer

k = 1.9/95

unklerhaukus · Answer

Why do you say that  `k isn't 0.02` ?

lxelle · Answer

Oh lol sorry lol. My wrong.

unklerhaukus · Answer

all sorted then?