IBDP Mathematics Applications & Interpretations SL Chapter 10 Notes

Modelling Rates of change: Exponential and logarithmic functions

STUDY NOTES FOR MATHEMATICS – Chapter 10 Modelling Rates of change: Exponential and logarithmic functions

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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e. This chapter in Math AA HL deals with the following: Rational exponents, Algebraic expansion and factorization, Exponential equations, Exponential functions, Growth and decay and the natural exponential. Rational Exponent uses the laws of exponents to prove for any integers. Algebraic expansion and factorization are learning to use standard rules of algebra, together with the laws of exponents, to simplify expressions containing rational or variable exponents. Exponential equations deal with learning to solve exponential equations and logarithms. In exponential functions you will learn to graph exponential equations on a graphing calculator, you will learn about asymptotes and investigating slopes. Growth and Decay will look at situations where quantities are either increasing or decreasing exponentially. The natural exponent termed “e” will also be discussed. Logarithms is an inverse of the exponential functions. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. The chapter is divided into the following: Logarithms in base 10, Logarithms in base a, Laws of logarithms, Natural logarithms, Logarithmic equations, The change of base rule, solving exponential equations using logarithms and Logarithmic functions. The first two chapters talk about logarithms with different bases. Laws of logarithms goes into investigation and proofing of logarithmic equations. Natural logarithms involve the natural exponent “e” and its inverse ln. Logarithmic equations are about solving the equations and turning non logarithmic equations to logarithmic ones, exponents can also be solved using logs. The change of base rule is changing the base of the log to solve the equation. Logarithmic functions are used for graphing.