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**EXERCISE 10.8**

**1. The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours?**

**2. Find the population of a city at any time t, given that the rate of increase of population is proportional to the population at that instant and that in a period of 40 years the population increased from 3,00,000 to 4,00,000.**

**3. The equation of electromotive force for an electric circuit containing resistance and self-inductance is E = Ri + L dt/di , where E is the electromotive force is given to the circuit, ℝ the resistance and L, the coefficient of induction. Find the current i at time t when E = 0.**

**4. The engine of a motor boat moving at 10 m / s is shut off. Given that the retardation at any subsequent time (after shutting off the engine) equal to the velocity at that time. Find the velocity after 2 seconds of switching off the engine.**

**5. Suppose a person deposits ₹10,000 in a bank account at the rate of 5% per annum compounded continuously. How much money will be in his bank account 18 months later?**

**6. Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. What percentage of the original radioactive nuclei will remain after 1000 years?**

**7. Water at temperature 100 º C cools in 10 minutes to 80º C in a room temperature of 25º C . Find**

**(i) The temperature of water after 20 minutes**

**(ii) The time when the temperature is 40º C**

**[ loge (11/15) = −0.3101; loge 5 = 1.6094 ]**

**8. At 10.00 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby Kitchen counter to cool. At this instant the temperature of the coffee was 180º F, and 10 minutes later it was 160º F . Assume that constant temperature of the kitchen was 70 º F .**

**(i) What was the temperature of the coffee at 10.15A.M.? [ log(9/11) = −0.6061]**

**(ii) The woman likes to drink coffee when its temperature is between 130 º F and 140 º F between what times should she have drunk the coffee? [log (6/11) = - 0.2006]**

**9. A pot of boiling water at 100 º C is removed from a stove at time t = 0 and left to cool in the kitchen. After 5 minutes, the water temperature has decreased to 80 º C , and another 5 minutes later it has dropped to 65 º C . Determine the temperature of the kitchen.**

**10. A tank initially contains 50 litres of pure water. Starting at time t = 0 a brine containing with 2 grams of dissolved salt per litre flows into the tank at the rate of 3 litres per minute. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. Find the amount of salt present in the tank at any time t > 0 .**

**1. After 10 hours the number of bacteria as 9 times the original number of bacteria.**

**2. P = 300000 (4/3)t/40**

**3. i = Ce – Rt/L**

**4. v = 10/e2**

**5. P = 10000e0.075**

**6. 910/108 % of the radioactive element will remain after 1000 years.**

**7. (i) 65.33ºC (ii) 51.91 mts**

**8. (i) T ≈ 151ºF (ii) t = 22.523. She drunk the coffee between 10.22 and 10.30 approximately.**

**9. 20º**

**10. x = 100 ( 1− e − 3t/50)**

Tags : Problem Questions with Answer, Solution , 12th Maths : UNIT 10 : Ordinary Differential Equations

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12th Maths : UNIT 10 : Ordinary Differential Equations : Exercise 10.8: Applications of First Order Ordinary Differential Equations | Problem Questions with Answer, Solution

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