The populations, P, of six towns at time t in years are given by(i) P=2,090(1.08)t(ii) P=560(1.12)t(iii) P=2,700(0.9)t(iv) P=1200(1.18)t(v) P=800(0.78)t(vi) P=2000(0.99)t (a) Which towns are growing in size? Which are shrinking? Select all that apply.Growing towns: (i) (ii) (iii) (iv) (v) (vi) Shrinking towns: (i) (ii) (iii) (iv) (v) (vi) (b) Which town is growing the fastest? What is the annual percent growth rate for that town?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is growing the fastest. It is growing at a rate of % per year. (c) Which town is shrinking the fastest? What is the annual percent decay rate for that town? Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is shrinking the fastest. It is shrinking at a rate of % per year. (d) Which town has the largest initial population (at t=0)? Which town has the smallest?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the largest initial population (given by ), and town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the smallest initial population (given by ).
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 at time t in years are given by
(i) P=2,090(1.08)t
(ii) P=560(1.12)t
(iii) P=2,700(0.9)t
(iv) P=1200(1.18)t
(v) P=800(0.78)t
(vi) P=2000(0.99)t
(a) Which towns are growing in size? Which are shrinking? Select all that apply.
Growing towns:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Shrinking towns:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(b) Which town is growing the fastest? What is the annual percent growth rate for that town?
Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is growing the fastest. It is growing at a rate of % per year.
(c) Which town is shrinking the fastest? What is the annual percent decay rate for that town?
Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is shrinking the fastest. It is shrinking at a rate of % per year.
(d) Which town has the largest initial population (at t=0)? Which town has the smallest?
Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the largest initial population (given by ), and town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the smallest initial population (given by ).
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