The Black-tailed prairie dog was decimated in Arizona in the 1960s due to a disease. A large part of the population, which was at carrying capacity, was killed. Only 10% survived. How long would it take with a regrowth rate of 2% to back to the carrying capacity? How many years will it take for the same situation if we double the regrowth due to improved ecosystems and double the initial amount of prairie dogs by importing prairie dogs from New Mexico?

Question

Mathematics

Cara George

2 December, 02:28

The Black-tailed prairie dog was decimated in Arizona in the 1960s due to a disease. A large part of the population, which was at carrying capacity, was killed. Only 10% survived. How long would it take with a regrowth rate of 2% to back to the carrying capacity? How many years will it take for the same situation if we double the regrowth due to improved ecosystems and double the initial amount of prairie dogs by importing prairie dogs from New Mexico?

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Answers (1)

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Finn Camacho · Answer 1

116.3, 41.05

Step-by-step explanation:

Using the growth rate formula

Final = initial (1 + rate) ^n

Rate = 2% = 0.02

n = number of years

Carry capacity = 100% (the original state before the disease) = final

100% = 1

1 = 0.1 (1+0.02) ^n

10 = (1.02) ^n

Log 10 / Log 1.02 = 116.3 = n

b) initial rate doubled = 0.02*2 (2%*2) = 0.04

Initial population doubled by importation = 0.1 * 2 = 0.2

Again, 1 = 0.2 (1+0.04) ^n

5 = 1.04^n

Log 5 / Log 1.04 = 41.05 = n