# calculus

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The population of a country was 8.4 million people in 2000. Three years later, the population of the same nation was 9.3 million people. Assuming that population is growing exponentially, what is the projected population (rounded to one-tenth of a million) of the country in 2008?

• calculus -

Just plug the numbers into the good old eponential growth formula:

P(t) = Po * e^rt
P(0) = 8.4 so Po = 8.4

P(t) = 8.4 e^rt
P(3) = 9.3 = 8.4 e^3r
9.3/8.4 = e^3r
ln 1.107 = 3r
r = ln 1.107/3 = 0.0339

P(t) = 8.4 e^.0339t
P(8) = 8.4 e^0.271 = 11.0

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