Exponential and logarithmic graphs and models
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Growth that feeds itself
- The exponential graph
- The logarithm graph
Read the transcript of the teaching part
Last time
Before we start: last time, in Simultaneous equations, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Growth that feeds itself
A bank balance, a virus, a viral video. The bigger it is, the faster it grows. That is exponential growth. And its mirror image, the logarithm, tells you how long that growth takes.
The exponential graph
The graph of y equals e to the x passes through zero, one. At x equals zero, any power is one. It is always above the x axis. As x gets very negative, it gets closer and closer to zero. The x axis is a horizontal asymptote. As x grows, the curve climbs ever more steeply. Its gradient equals its height.
The logarithm graph
The natural logarithm is the inverse of the exponential. So its graph is the reflection in y equals x. It passes through one, zero. Only positive x is allowed. The y axis is a vertical asymptote. As x tends to zero from the right, the curve plunges.
Chapter 6: Logarithmic and exponential functions
- Exponential and logarithmic graphs and models 5 min
- Laws of logarithms and solving equations 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.