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A security light shines on a car park as shown in the diagram below. A sighting of the top of the light is taken from two different positions, A and B, in the car park. The angle of elevation from A is 30 deg and from B is 50 deg. If the horizontal distance between A and B is 200 metres find the height of the top of the security light.

Investigating the three functions

y = e^x

y = x

y = ln x

create a table to work out the values for each function, using a range of values for x from - 4 to 4 and only plot those points where y is between 10 an - 4, plot the three functions on the same axes, remembering to label which line represents which function and use the same size scale on both x and y axis.

What do you notice about the graphs of these functions?