The population of a country was 76 million in 2007 and the continuous exponential growth rate was estimated at 2.6% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 2013. Round your answer to 1 decimal place. The approximate population in 2013 is?
Question
The population of a country was 76 million in 2007 and the continuous exponential growth rate was estimated at 2.6% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 2013. Round your answer to 1 decimal place. The approximate population in 2013 is?
Solution
To solve this problem, we will use the formula for continuous exponential growth, which is:
P = P0 * e^(rt)
where: P is the future population, P0 is the initial population, r is the growth rate, and t is the time in years.
Given in the problem: P0 = 76 million, r = 2.6% = 0.026 (converted from percentage to decimal), and t = 2013 - 2007 = 6 years.
Substituting these values into the formula, we get:
P = 76 * e^(0.026 * 6)
Now, calculate the value of e^(0.026 * 6) using a calculator. Then multiply the result by 76 to get the future population.
After calculating, you should get the approximate population in 2013. Remember to round your answer to 1 decimal place.
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