Exercise 1.5 Class 12 Math Solutions - Unit 1 Graphical Representation of Functions, Punjab Board
Step-by-step solutions to Exercise 1.5, Unit 1: Graphical Representation of Functions, for Class 12 Punjab Board students. Covers real-life applications of exponential and logarithmic functions-including population growth, radioactive decay, decibel sound intensity scales, discrete compound interest, and continuous compound interest-worked out question by question.
Exercise Overview
Exercise 1.5 concludes Unit 1 of Class 12 Mathematics by showcasing the practical applications of exponential and logarithmic functions in real-world physical, financial, and scientific scenarios under the Punjab Board PCTB / PECTAA curriculum. The exercise bridges abstract functional mathematics with applied modeling, illustrating how exponential rates govern population dynamics, bacterial growth, and radioactive decay half-life calculations through N(t) = N₀·e^(kt).
In acoustics and physics, students apply logarithmic scales to quantify sound intensity in decibels using β = 10 · log₁₀(I / I₀), learning how logarithmic compression handles vast ranges of sound power. In financial mathematics, the exercise covers discrete compound interest A = P·(1 + r/n)^(n·t) alongside continuous compound interest A = P·e^(rt). Students learn to solve for accumulation periods, effective interest yields, and doubling time by applying natural logarithms.
For Punjab Board HSSC Part 2 examinations across all nine divisions (Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, Bahawalpur, Sargodha, Sahiwal, and D.G. Khan), Exercise 1.5 is a frequent source of applied long questions and conceptual word problems. These step-by-step solutions guide students through formula selection, variable substitution, and algebraic isolation, ensuring thorough exam preparation.