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These are the Transum resources related to the statement: "Exponential functions and their graphs: f(x)=a^{x}, a>0, f(x)=e^{x}. Logarithmic functions and their graphs: f(x)=log_{a}x, x>0, f(x)=lnx, x>0".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Indices A self marking exercise on indices (powers) including evaluating statements and solving equations.
- Logarithms Self-marking exercises on evaluating logarithms and using them to solve equations.

Here are some exam-style questions on this statement:

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*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 - "
*Find the value of the following:*" ... more - "
*Evaluate the following, giving your answers as integers.*" ... more - "
*Find the value of*" ... more - "
*(a) Solve \(4x^2 - 8x - 5 = 0\)*" ... more - "
*A cup of hot tea is placed on a table to cool. The temperature of the room is 24*" ... more^{o}C. - "
*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 - "
*Consider the function \(f (x) = \log_p(24x - 18x^2)\) , for \(0 \lt x \lt 1\), where \(p \gt 0\).*" ... more - "
*Fifty milligrams of a certain type of medicine has been shown to enter the bloodstream of an adult according to the following equations:*" ... more

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

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