Question

In a hypothetical human population of 1000 individuals showing exponential growth every female gives birth to 0.3 children per year. Death rate is 0.1 per capita per year. what will be the population size after 10years. (e=2.72). the answer is 1649. how do we arrive at this answer.

a) P(t) = 1000 * (0.3 - 0.1)t
b) P(t) = 1000 * (0.3 - 0.1)^t
c) P(t) = 1000 * (0.3 + 0.1)e^(-2.72t)
d) P(t) = 1000 * (0.3e^(-2.72t) - 0.1)

Answer 1

The population size after 10 years can be calculated using the equation P(t) = Po * e^(rt), where P(t) is the population size after time t, Po is the initial population size, e is approximately 2.72, and r is the growth rate. Using the given birth rate and death rate, the growth rate can be calculated as 0.2. Substituting the values into the equation, the population size after 10 years is 7380.

Step-by-step explanation:

The formula to calculate the population size after a certain number of years for a population showing exponential growth is given by the equation:

P(t) = Po * e^(rt)

where P(t) is the population size after time t, Po is the initial population size, e is approximately 2.72 (the base of the natural logarithm), and r is the growth rate.

In this case, the birth rate is 0.3 children per year and the death rate is 0.1 per capita per year. To calculate the growth rate (r), we subtract the death rate from the birth rate: r = 0.3 - 0.1 = 0.2. We can now substitute the values into the equation:

P(10) = 1000 * e^(0.2 * 10) = 1000 * e^2 = 1000 * 2.72^2 = 1000 * 7.38 = 7380

Therefore, the population size after 10 years is 7380.