a. Given that x < 5, find

b. A chemical reaction takes place between two substances A and B. When this happens, a third substance, C, is produced. After t hours there are 5 − x grams of A, there are 10 − x grams of B and there are x grams of C present. 

The rate of increase of x is proportional to the product of 5 − x and 10 − x. Initially, x = 0 and the rate of increase of x is 1 gram per hour.

i. Show that x and t satisfy the differential equation

ii. Solve this equation, giving x in terms of t.

iii. According to the model, approximately how many grams of chemical C are produced by the reaction?

Transcribed Image Text:

√ 50 (5-x)(10-x) dx.