Question

A population of deer mice consists of 200 individuals and has an r = 0.1. A population of wood rats consists of 100 individuals and has an r = 0.2. Which population is growing the fastest in terms of individuals per year? Assume the time period is 1 year.

Answer 1

Both populations of deer mice and wood rats are growing at the same rate of 20 individuals per year.

Step-by-step explanation:

In this scenario, the population of deer mice consists of 200 individuals with an r (population growth rate) of 0.1, and the population of wood rats consists of 100 individuals with an r of 0.2. To determine which population is growing faster in terms of individuals per year, we need to calculate the population growth for each population.

Population growth can be calculated using the formula:

Population Growth = r * N

Where r is the population growth rate and N is the initial population.

For the deer mice population:

Population Growth = 0.1 * 200 = 20 individuals per year

For the wood rats population:

Population Growth = 0.2 * 100 = 20 individuals per year

Both populations are growing at the same rate of 20 individuals per year.

Answer 2

Population of dice mice after one year = 2000

Population of wood rats after one year = 1000

The population of deer mice is growing faster than the popular of wood rats

Step-by-step explanation:

The expression for population = dN/dt = rN

Upon integration N = rN²/2

Therefore for population N = 200 and r= 0.1

N after one year = (0.1 x 200²)/ 2 = 2000

Therefore for population N = 100 and r= 0.2

N after one year = (0.2 x 100²)/ 2 = 1000

Hence the population of deer mice is growing faster than the popular of wood rats