A breeding group of foxes is introduced into a protected area and exhibits logistic population growth. After t years the number of foxes is given by N(t) = 37.5 0.25 + 0.76t foxes. (a) How many foxes were introduced into the protected area? foxes (b) Calculate N(6). (Round your answer to the nearest whole number.) N(6) = Explain the meaning of the number you have calculated. This means that after 6 years there were about foxes in the protected area. (c) Explain how the population varies with time. Include in your explanation the average rate of increase over the first 10-year period and the average rate of increase over the second 10-year period. The fox population is constant.The fox population is growing, but the population does not grow as rapidly in later years as it did early on. The fox population is growing, but the population does not grow as rapidly in early years as it did later on. (d) Find the carrying capacity for foxes in the protected area. foxes (e) As we saw in the discussion of terminal velocity for a skydiver, the question of when the carrying capacity is reached may lead to an involved discussion. We ask the question differently. When is 97% of carrying capacity reached? (Round your answer to the nearest year.) after years
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!
A breeding group of foxes is introduced into a protected area and exhibits logistic population growth. After t years the number of foxes is given by
| 37.5 |
| 0.25 + 0.76t |
foxes
(b) Calculate N(6). (Round your answer to the nearest whole number.)
N(6) =
Explain the meaning of the number you have calculated.
(c) Explain how the population varies with time. Include in your explanation the average rate of increase over the first 10-year period and the average rate of increase over the second 10-year period.
(d) Find the carrying capacity for foxes in the protected area.
foxes
(e) As we saw in the discussion of terminal velocity for a skydiver, the question of when the carrying capacity is reached may lead to an involved discussion. We ask the question differently. When is 97% of carrying capacity reached? (Round your answer to the nearest year.)
after years
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