Ex 9.4, 20 - Chapter 9 Class 12 Differential Equations

Transcript

Ex 9.4, 20 In a bank, principal increases continuously at the rate of % per year. Find the value of r if Rs 100 double itself in 10 years log 2=0.6931 Let Principle = p Given, principle increases ar rate r % per year = % P = 100 p = 100 dt Integrating both sides = 100 log p = 100 + log c log p log c = 100 log = 100 = e 100 Initially t = 0 and p = 100 100 = e .0 100 100 = e 0 100 = 1 c = 100 Put this in equation (1) 100 = e 100 Also, At t = 10, p = 200 200 100 = e 10 100 2 = e 10 log 2 = 10 0.6931 = 10 r = 6.931 Rate of interest = r = 6.931 %