EXERCISE 4.4 | DIFFERENTIAL EQUATIONS | Class 12 Math | FBISE | NBF

EXERCISE 4.4 | DIFFERENTIAL EQUATIONS | Class 12 Math | Federal Board | National book Foundation Welcome to Exercise 4.4 of Differential Equations for Class 12 Mathematics (Federal Board, National Book Foundation). In this lecture, we solve real-life application problems using first-order differential equations such as population growth, radioactive decay, Newton’s Law of Cooling, and motion under gravity. This video is perfect for Class 12 students preparing for exams and teachers who need clear, step-by-step explanations. TIMESTAMPS 00:00:00 - Q1. Population growth model (Thomas Malthus). Present population 20 million and 25 million after 4 years. Find the population after 12 years. 00:14:33 - Q2. Newton’s Law of Cooling. Pizza cooling from 150°C to 90°C in 4 minutes. Find time to reach 40°C at room temperature 20°C. 00:27:57 - Q3. Bacteria growth proportional to population. Population becomes four times in 2 days. Find population after 10 days if initial population is 20. 00:35:33 - Q4. Radioactive decay. Initial amount 50 g, half-life 1000 years. Find amount after 800 years. 00:44:27 - Q5. Thermometer cooling. Room temperature 80°F, placed on ice at 30°F. Temperature becomes 40°F in 1 minute. Find time to reach 70°F. 00:53:34 - Q6. Motion under gravity. Ball thrown upward with 40 m/s. Form the differential equation, find velocity after 1 second, and maximum height. Air resistance neglected. ABOUT THIS LECTURE In Exercise 4.4, we cover: • Population growth and decay models • Newton’s Law of Cooling • Radioactive decay and half-life calculations • Growth of bacteria using exponential models • Motion under gravity and differential equations • Step-by-step solutions from National Book Foundation • Fully exam-oriented explanation for Federal Board students Hashtags #Class12Math #DifferentialEquations #Exercise4_4 #FBISE #NationalBookFoundation #MathLecture #PopulationGrowth #NewtonLawOfCooling #RadioactiveDecay #Class12FederalBoard Class 12 Math, Differential Equations, Exercise 4.4, Federal Board, FBISE Math, National Book Foundation Math, Population Growth Problem, Newton Law of Cooling, Radioactive Decay Math, Motion Under Gravity, Class 12 Maths Pakistan, Homogeneous Equations, Exponential Growth and Decay, Math Lecture Urdu, Class 12 Problems Solution, Differential Equation Applications, Pakistani Students Math, FSC Math Part 2, NBF Math Chapter 4