General Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — Exponential function and its applications

About this lesson

This unit introduces the exponential function, defined as f(x) = a^x where a is a positive real number not equal to 1. It explains that the independent variable (x) is the power while the base is a real number, contrasting with algebraic functions where x is the base. The unit covers graphical representation of exponential functions for cases a > 1 (growth) and 0 < a < 1 (decay), using examples like f(x) = 2^x and g(x) = (1/2)^x. It derives properties from graphs: functions are increasing if a > 1, decreasing if 0 < a < 1, the range is R+ (positive reals), and the curve of f(x) = a^x is the reflection of g(x) = (1/a)^x across the y-axis. Students practice graphing, finding domain and range, identifying increasing/decreasing behavior, and solving problems involving function values and transformations. The unit mentions real-life applications such as banking profits, overpopulation, cell reproduction, and half-life of radioactive atoms, but does not delve into specific calculations.

Main topics in this lesson

  • Definition of exponential function
  • Graphical representation
  • Properties of exponential functions (increasing/decreasing, range, reflection)
  • Applications in daily life (banking, population, cell reproduction, half-life)

Key terms and vocabulary

  • Exponential function
  • Exponential growth
  • Exponential decay
  • Base
  • Power
  • Domain
  • Range
  • Increasing function
  • Decreasing function
  • Reflection on y-axis

Questions and answers on Exponents, Logarithms and their Applications — Exponential function and its applications - practice and revision

Multiple choice questions on this lesson in General Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

منحنى الدالة f(x) = (1/5)^x هو انعكاس لمنحنى الدالة g(x) = 5^x حول:

  • 1 محور الصادات
  • 2 محور السينات
  • 3 نقطة الأصل
  • 4 المستقيم y = x
2

أي مما يأتي يعد تطبيقاً من تطبيقات الدالة الأسية في الحياة اليومية؟

  • 1 حساب الفائدة البنكية
  • 2 حساب محيط المثلث
  • 3 حساب مساحة الدائرة
  • 4 حساب حجم المكعب
3

الدالة الأسية f(x) = (3/4)^x تكون:

  • 1 تناقصية
  • 2 تزايدية
  • 3 ثابتة
  • 4 غير معرفة
4

إذا كانت f(x) = 10^x، فإن قيمة f(-1) تساوي:

  • 1 1/10
  • 2 -10
  • 3 -1/10
  • 4 10
5

أي الدوال الآتية تمثل تحللاً أسياً؟

  • 1 g(x) = (1/4)^x
  • 2 g(x) = 4^x
  • 3 g(x) = x^4
  • 4 g(x) = 4x
6

أي الدوال الآتية تمثل نمواً أسياً؟

  • 1 f(x) = 2^x
  • 2 f(x) = (1/2)^x
  • 3 f(x) = x^2
  • 4 f(x) = 2x

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