The population P (in thousands) of a new town is modelled by the relationship P = ka^t where t is the time in years. Its growth over the first five years is shown in the table below.

a. Explain why you would expect that the graph of ln P against t to be a straight line.

b. Draw up a table of values, plot the graph and use it to estimate values for a and k to 1 d.p.

c. Using these values, calculate an estimate for the population after 20 years. How accurate is this likely to be?

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Year (f) 1 1 2 3 4 Population (P) 3.6 4.3 5.2 6.2 7.5