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This problem says the population of a country was 71 million in 1987, and the continuous exponential growth rate was estimated at 3 .3 % per year.
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Assuming that the population of the country continues to follow that exponential growth model, we want to, for a, determine an exponential model that represents this population t years after 1987 in terms of millions of people.
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B wants us to then use that model to find the projected population in 1994, and then finally we want to find the number of years for the population to grow to 283 million.
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So the first thing we need to do is use the correct model for our function, and the model we're going to use is p of t.
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And since we're growing continuous exponential growth, we're going to show that this is equal to a, where a could be our initial amount times e raised to the rt.
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And our a value will be 71 for the 71 million in this case.
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E will stay a part of our function.
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Our rate is going to replace r, but in its decimal form, so 0 .033, raised to the 2 .1 million.
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T where again t is a number of years after 1987.
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So this is our function to represent the population.
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So that's our answer for a.
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And then for b, we want to use this function to predict the population in 1994.
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So in 1994, there are seven years that have passed since 1987.
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So we're evaluating at seven equal to 71 times e...