18) The populations, P, of six towns with time tt in years are given by 1 P=1900(1.195)tP=1900(1.195)^t 2 P=2800(0.8)tP=2800(0.8)^t 3 P=600(1.17)tP=600(1.17)^t 4 P=1200(1.08)tP=1200(1.08)^t 5 P=700(0.79)tP=700(0.79)^t 6 P=2300(0.96)tP=2300(0.96^)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. (a) Which of the towns are growing? (b) Which of the towns are shrinking? (c) Which town is growing the fastest? What is the annual percentage growth RATE of that town?( ) % (d) Which town is shrinking the fastest? What is the annual percentage decay RATE of that town?( ) % (e) Which town has the largest initial population? (f) 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!
18) The populations, P, of six towns with time tt in years are given by
| 1 | P=1900(1.195)tP=1900(1.195)^t |
| 2 | P=2800(0.8)tP=2800(0.8)^t |
| 3 | P=600(1.17)tP=600(1.17)^t |
| 4 | P=1200(1.08)tP=1200(1.08)^t |
| 5 | P=700(0.79)tP=700(0.79)^t |
| 6 | P=2300(0.96)tP=2300(0.96^)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.
(a) Which of the towns are growing?
(b) Which of the towns are shrinking?
(c) Which town is growing the fastest?
What is the annual percentage growth RATE of that town?( ) %
(d) Which town is shrinking the fastest?
What is the annual percentage decay RATE of that town?( ) %
(e) Which town has the largest initial population?
(f) Which town has the smallest initial population?
19) The "net up" counter (using technology to count fish passing upstream) at Roe River42 showed that there were 58115811 fish in 2005, but that number dropped by 19041904 fish in 2010. Compute the percentage change from 2005 to 2010: ( ) %.
20) Let GG be an exponential function that is changing at a rate proportional to itself, with constant of proportionality 0.6
(a) What's the growth factor of G?
24) A researcher believes that if x thousand individuals among a susceptible population are inoculated (made no longer susceptible to a disease), then a function of form
for constants a, b, and R would model the eventual number of infected individuals (also in thousands). Let R=0.9
(a) If the susceptible population is 5000 and no one is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , )
(b) If the susceptible population is 5000 and everyone is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , )
(c) Use the results of parts (a) and (b) to find approximate values for the constants
a= ( )
and b= ( ) in the researcherâs model.
(d) According to the model, how many susceptible individuals will be infected if half of them are inoculated?
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