The population of a city was 320,000 in the year 2000. By 2012, the population reached 360,800. a. Write a model of the form P(t) = P0ekt to represent the population P(t) for a time t years since 2000. b. Approximate the population in the year 2015 assuming that this trend continued. Round to the nearest 100 people. c. Determine the amount of time for the population to reach 400,000 if this trend continues. Round to the nearest tenth of a year.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The population of a city was 320,000 in the year 2000. By 2012, the population reached 360,800.
a. Write a model of the form P(t) = P0ekt to represent the population P(t) for a time t years since 2000.
b. Approximate the population in the year 2015 assuming that this trend continued. Round to the nearest 100 people.
c. Determine the amount of time for the population to reach 400,000 if this trend continues. Round to the nearest tenth of a year.
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