The populations, P, of six towns with time t in years are given by 1 P=1700(0.98)t 2 P=2100(0.8)t 3 P=1400(1.189)t 4 P=700(0.78)t 5 P=1100(1.03)t 6 P=600(1.14)t Answer the following questions regarding the populations of the six towns above. Whenever you need to enter several towns in one answer, enter your answer as a comma separated list of numbers. For example if town 1, town 2, town 3, and town 4, are all growing you could enter 1, 2, 3, 4 ; or 2, 4, 1, 3 ; or any other order of these four numerals separated by commas. Which of the towns are growing? Which of the towns are shrinking? Which town is growing the fastest? What is the annual percentage growth RATE of that town? Which town is shrinking the fastest? What is the annual percentage decay RATE of that town? Which town has the largest initial population? Which town has the smallest initial population?
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 populations, P, of six towns with time t in years are given by
| 1 | P=1700(0.98)t |
| 2 | P=2100(0.8)t |
| 3 | P=1400(1.189)t |
| 4 | P=700(0.78)t |
| 5 | P=1100(1.03)t |
| 6 | P=600(1.14)t |
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