Exponential Growth & Decay (Cambridge International AS Mathematics)

Exponential growth & decay

What is exponential growth?

• y = Ae^kt is exponential growth

What is exponential decay?

• y = Ae^-kt is exponential decay

• k > 0 so plus or minus sign in equation immediately indicates growth or decay
• A is the starting value or initial value, when t = 0
• t is often used, rather than x, as many models are time-dependent

How do I write a^x in terms of e^x?

• Using e makes the maths easier

• With the proper choice of k, all exponential functions of the form a^x can be written in the form e^kx

  • a^x= e^kx

How are e^x and ln x inverses of each other?

• ln is the inverse of e

• The graph of y = ln x is the reflection of the graph of y = e^x in the line y = x

Worked Example