Part2 Continuous and Discrete Exponential Growth Exponential growth models are t

Question

Part2 Continuous and Discrete Exponential Growth Exponential growth models are the simplest way in which to conceptualize populations growing in an environment with unlimited resources over times. For populations that grow continuously throughout the year, we use the instantaneous rate of growth (r). However, some populations have specific periods of time in which births occur, and for these populations, we use lambda (lambda) to describe the discrete growth rate. Please use the following equations to solve the following problems pertaining to exponential growth. N(t) = N_ce^rt dN/dt = r N lambda = e^r N(t) = N_e lambda' ln (x^5) = y ln (x) In c = 1 A population of mice continuously breed over the year. A small population colonizes an island with plenty of food and no predators and their population begins to grow exponentially. if the original population size colonizing the island is made up of 40 individuals, and the intrinsic growth rate is 0.3, how many mice will be on the island in 4 years? After many years, this same population undergoes a reproductive mutation that causes females only to breed in the Spring. Using the information on instantaneous growth rate defined in problem 5. How long would it take for a population of 100 of these new mutated individuals to grow to 400 individuals? How long will it take for a population of continuously breeding red-legged tree frogs to double using the exponential growth model if their instantaneous growth rate is 0.2?

Explanation / Answer

5) The mice population is under exponential growth.

Therefore, the growth rate is given by the formula,

N(t) = Noe rt

= 40 x e (0.3)(3)

= 40 x e 0.9

= 40 x 2.46

= 98.4

Mice population after 3 years is 98

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