Question

A tank contains 1767 kg of compound X. Each year, a fixed amount of 12 kg of the

compound leaks out of the tank. In addition, compound X also degrades to compound Y, at
a constant rate of 0.012 mass fraction per year (do not confuse mass fraction with percent).
After 7 years, how many kilograms of compound X remain in the tank?

Answer 1

After 7 years, the amount of compound X that will remain in the tank can be calculated as follows:

Total amount of compound X initially = 1767 kg

Amount of compound X leaked out every year = 12 kg

Total amount of compound X leaked out in 7 years = 12 kg/year x 7 years = 84 kg

Amount of compound X that degrades to Y in one year = 0.012 x 1767 kg = 21.204 kg

Amount of compound X that remains after 7 years = 1767 kg - 84 kg - 7 x 21.204 kg
= 1486.172 kg (rounded to three decimal places)

Therefore, after 7 years, approximately 1486.172 kg of compound X will remain in the tank.