Chapter 9 Differential Equations Ex 9.4 Solutions
Question - 21 : - Ina bank, principal increases continuously at the rate of 5% per year. An amountof Rs 1000 is deposited with this bank, how much will it worth after 10 years
.
Answer - 21 : -
Let p and t bethe principal and time respectively.
Itis given that the principal increases continuously at the rate of 5% per year.
Integratingboth sides, we get:
Now, when t = 0, p =1000.
⇒ 1000 = eC … (2)
At t = 10, equation (1)becomes:
Hence,after 10 years the amount will worth Rs 1648.
Question - 22 : - Ina culture, the bacteria count is 1,00,000. The number is increased by 10% in 2hours. In how many hours will the count reach 2,00,000, if the rate of growthof bacteria is proportional to the number present?
Answer - 22 : -
Let y be the number ofbacteria at any instant t.
Itis given that the rate of growth of the bacteria is proportional to the numberpresent.
Integratingboth sides, we get:
Let y0 be the number ofbacteria at t = 0.
⇒ log y0 = C
Substitutingthe value of C in equation (1), we get:
Also,it is given that the number of bacteria increases by 10% in 2 hours.
Substitutingthis value in equation (2), we get:
Therefore,equation (2) becomes:
Now, let the time when the number ofbacteria increases from 100000 to 200000 be t1.
⇒ y = 2y0 at t = t1
Fromequation (4), we get:
Hence, in 
hoursthe number of bacteria increases from 100000 to 200000.
Question - 23 : - Thegeneral solution of the differential equation 
A.
B.
C.
D.
Answer - 23 : -
Integratingboth sides, we get:
Hence,the correct answer is A.