Exponential Functions (Edexcel IAL Maths)

Spec point — 5.1

Exponential functions

What are exponential functions?

• Exponential functions of the form y = a^x with a > 0 are considered at A level

What are exponential graphs?

• All graphs of the form y = a^x will pass through (0, 1) because a⁰= 1
• The x-axis is an asymptote

What is exponential growth?

• Where x < 0 the higher value of a is the “lower” graph

  • e.g. $3^{x}<2^{x}$ when $x<0$

• Where x > 0 the higher value of a is the “higher” graph

  • e.g. $3^{x}>2^{x}$ when $x>0$

• a > 1 is exponential growth(see Exponential Growth & Decay)

What is exponential decay?

• Where x < 0 the higher value of a is the “lower” graph

  • e.g. $0.3^{x}<0.2^{x}$ when $x<0$

• Where x > 0 the higher value of a is the “higher” graph

  • e.g. $0.3^{x}>0.2^{x}$ when $x>0$

• 0 < a < 1 is exponential decay

• You may like to think about why a = 1 is not considered... If a = 1, y = 1^x = 1 for all values of x

Worked Example