Question

. Suppose you have a population of mammals growing with abundant resources. The mammals can only reproduce during one breeding season per year. In 2018, the population was 72 individuals. all your work. In 2019, the population was 84 individuals. Please show Is the population growing exponentially or geometrically? How do you know? а. b. What is the population growth rate parameter (A)? If the population continues to grow at this rate, how many organisms will there be in c. 2021?

Answer 1

a) The population is growing geometrically. When a population have distinct reproductive season it is not growing continuously & will have discrete reproductive periods. This type of growth show geometric growth. As the mammals only reproduce one breeding season per year, it has distinct reproductive season. From this we can tell that the mammals undergo geometric growth.

b) The population growth rate is the ratio of population (N_t+1) in (t+1) year to the population (N_t) in t year.

Given, Population in 2019 (N_t+1) = 84, Population in 2018 (N_t) = 72

So, population growth rate ($\lambda$) = N_t+1 / N_t = 84/72 = 1.1667 (Up to 4 decimal)

c) We know that, N_t = N₀$\lambda$^t where, N_t = Population at t year, N₀ = Initial population, t = time in year, $\lambda$ = Population growth rate

Given, N₀ = 84 (Population in year 2019), $\lambda$ = 1.1667 (Calculated in previous part, t = 2 year (As difference between 2021 & 2019 is 2 years)

So, population in 2021 (N_t) = 84 x (1.1667)² = 114.34 $\approx$114