Question

1. Suppose that a population of deer is experiencing exponential growth, with r= 1.5 individuals/year. If the population size now is 4, how many deer will be added to the population in the next year? If necessary, truncate your answer to a whole number. Show your work.
2. Suppose that a population of deer is experiencing exponential growth, with r= 0.89 individuals/year. If the starting population size was 8, how many deer will be in the population after 5 years? If necessary, truncate your answer to a whole number. Show your work.
3. Suppose that a population of 50 deer lives on the UCONN campus. If these deer have an intrinsic growth rate (r) of 0.65 individuals/year, and if their population grew exponentially, how many years would it take the population to double in size? Show your work and report your answer to 2 decimal places.
4. Suppose a population of deer is experiencing density-dependent growth. If the carrying capacity is 100 deer and r = 0.25 individuals/month, how many deer will be added to the population during the next month when the population size is 20? Show your work and report your answer to 2 decimal places.
5. Suppose a population of deer is experiencing density-dependent growth. If the carrying capacity is 120 deer and r = 0.10 individuals/month, what is the maximum possible population growth rate, expressed as number of deer added per month, of the population? Show your work and report your answer to 2 decimal places.

Answer 1

Answer 1:

Given,

Population growth rate, r = 1.5

Population size, N = 4

For a population growing exponentially, the rate of change of population size, dN/dt = rN.

= 1.5 × 4

= 6

Thus, after one year 6 deers will be added to the population.

Answer 2:

Given,

r = 0.89

Initial population size, N = 8

Time, t = 5 years.

For a population growing exponentially, the size of population N' after time "t" can be determined as:

N' = Ne^rt

= 8 × e ^{(0.89 × 5)}

= 8 × e^4.45

= 8 × 85.63

= 685.

This, after five years, the population size would be 685.