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These are the Transum resources related to the statement: "Understand and use exponential growth and decay; use in modelling (examples may include the use of e in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth); consideration of limitations and refinements of exponential models".

Here are some exam-style questions on this statement:

• "Sketch the graph of \(y=0.5^x +1\) for \(0 \le x \le 5\) labeling the y intercept." ... more
• "While studying a new disease, scientists found that the number of toxic cells in the bloodstream increased over time, according to the model \(D(t)=12×(1.16)^t , t \ge 0\) where \(D\) is the number of the toxic cells in the bloodstream per litre and \(t\) is the time in hours." ... more
• "Percy Cod and Fran Finklestein are both researchers working at different universities. They are each studying a different colony of bacteria which coincidentally start increasing in size at the same time." ... more
• "The diagrams above show a growing fractal of triangles. The sides of the largest equilateral triangle in each diagram are of length 1 metre." ... more
• "The quantity of heat required to heat an amount of water is given by the formula:" ... more
• "Doctor Octothorpe investigated the decreasing population of a colony of ants in a remote province of China. His investigation took place in 1958." ... more
• "In a remote lake it was noticed by conservationists that a disease was rapidly spreading amongst two species of fish, R and S, which is reducing their numbers. The conservationists calculated that the numbers of each type of fish can be modelled by the functions:" ... more

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Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Indices Where do many fish live? Indices (in the seas!) This topic involves the use of the index, power or exponent. The concept is easily misunderstood and a surprisingly large number of pupils will evaluate 62 as 12 and not 36. After having mastered positive integer indices pupils should move on to negative indices and fractional indices. Exploring this topic in both numeric and algebraic ways will provide understanding and competence in this important concept.