Exponential Functions

Success Criteria

At the end of this chapter, students are able to:

  1. Simplify exponential expressions.

  2. Solve exponential equations using comparison of powers.

  3. Solve exponential equations using the substitution method.

  4. State and appreciate Euler's Number, e.

  5. Use exponential functions to model real-world problems (AO2).

Recap

In the previous chapter, we learnt about polynomials. Polynomials are of the form, ax, where the variable is the base of the term. An exponential has a similar form, abˣ, but the variable is now the exponent of the term.

Polynomial vs Exponential Functions

Introduction

An exponential function is characterised by its rate of growth to be dependent on its current value. Embedded within exponential functions is some sort of doubling or halving effect.

Eg. Zombies. The rate at which the number of zombies increase (in movies) depend on the existing number of zombies in the population.

1 becomes 2. 2 becomes 4. 4 becomes 8 and so on.

Next: Let's review the Indice laws again.