A population of 3.2 million grows at a constant percentage rate, What is the pop

Question

A population of 3.2 million grows at a constant percentage rate, What is the population one century later if there is: An annual growth rate of 2% A continuous growth rate of 2% per year Explain how you can tell which of the answers would be larger before doing the calculations. The gross domestic product (GDP) of Chile was 145.8 billion dollars in 2007 and was growing at a continuous rate of 5.1% per year. Find a formula for G, the GDP of Chile in billion dollars, as a function of t, the number of years since 2007. Use your answer to part (a) to calculate the growth factor of the exponential function. That is write a formula for G as a function of t using the form G = ab^t. By what percent does the GDP increase each year? Graph your answers to part (a) and part (b) on the same axes. Explain what you see.

Explanation / Answer

6. a) i) population is 3.2 million

annual growth rate = 2%

So, population after 100 years = 3.2*(1.02)^100

Which is = 23.18 million

ii) Exponential growth = Pe^rt

So, population after 100 years = 3.2*e^.02*100 = 23.64 million

b) Annual growth rate increases linearly over time but continuous growth happens exponentially and has a geometric growth. That's why continuous rate of growth is always higher.

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