Question

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Question 2. Exponential population growth model:

N_t = N₀ * e^r_m*t

where:

N_t = population size at time t

N₀ = starting population size

e = 2.7183 (Euler’s number)

r_m = estimated rate of increase

Use the above exponential growth model to solve the following for a (not so) get rich quick scheme to breed worms in your apartment and sell them as fishing bait. You start your project with only five individuals.

2a. If your estimated rate of increase (r_m) is 0.19 per day, what will your population size be in t = 10 days?

2b. If your estimated rate of increase (r_m) is 0.19 per day, what will your population size be in t = 30 days?

From your answers to 2a and 2b, the exponential nature of the increase in your worm population should be clear. However, in another 30 days you find that your population increase has leveled off (i.e., looks more like an S-shaped curve)

2c. What is the name of this type of growth curve?

2d. Assume that you have raised your earthworms in a defined area such as a fish tank. Name the constraint on population growth that your worms have probably reached, and describe one likely mechanism behind this constraint.

Answer 1

Sol: since, [Nt = Nort) N = population size at time t No a starting population size - 2.7183 Tm. estimated rate of increase using the above mentioned growth equation, (a) when son = 0.19 per day, No: 5 t. 10 days population size after 10 days will become, Nt. 5 0 19410 Talring to N & 5 X 6.685 = 33.425 ~ 34 days So, after 10 days , population size becomes 34. (6) when sm= 0.19 per day & No: 5 , 30 days N. N = 5 * 0.19 +30 5 5.7 - 298.86 Nt & 299 days (c) There 2 types of growth cowe, logistic growth awe and J- shaped growth nowe. Worm population exhibit grow the corre as it follows a s-shaped growth pattern.

(d) when earthworms are raised in a defined area, for example a fish tank, the growth can be restricted due to soul (i) Temperature - In order to survive and breed, earthworms require temperature ranging from 55 and 85°F. So, it is necessary to maintain the bed temperatwee according to the optimum range to promote cocoon production and watching. () Oxygen - It is necessary to maintain a minimum level of dissolved oxygen, as lack of oxygen can lead to death of earthworms. OU 00