The rate of decay of mass of certain substance at time tis proportional to the tt that instant. The time during which the original mass of m₀ gram will be leftht m_ , gram is (k is constant of proportionality

Step-by-step solution

Let m be the initial mass of substance at time t . array l dm dt km dm dt =- km dm m = - k dt m =- kt + c ....(1) When t =0, ~m = m ₀ we get m ₀=0+ c c = m ₀ From (1), ( m m ₀ )=- kt t = -1 k ( m m ₀ ) array array l When m=m₁ , we get aligned t &= -1 k ( m₁ m₀ ) t= 1 k ( m₀ m₁ ) aligned array