Question

1. there are 2,000 mice living in a field. if 1,000 mice are born each month and 200 mice die each month, what is the per capita growth rate of mice over a month? round to the nearest tenth.
2. the doubling time of a population of plants is 12 years. assuming that the initial population is 300 and that the rate of increase remains constant, how large will the population be in 36 years?
3. suppose that 50 fish are born in year 1. there are only 36 left in year 2 and 22 left in year 3. what is the mortality rate between years 2 and 3? round to the nearest hundredth.
4. you and your friends have monitored two populations of wild lupine for one entire reproductive cycle (june year 1 to june year 2). by carefully mapping, tagging, and taking a census of the plants throughout this period, you obtain the data listed in the chart.

parameter	population a	population b
number of new seedlings established	100	30
number of initial plants that die	20	100

a. calculate the following parameters for each population. round each to whole number or hundredth where applicable and record your answers here (no grids provided.)

parameter	population a	population b
d (deaths during time interval)
b (per capita birth rate)
d (per capita death rate)
r (per capita rate of increase)

Explanation:

10.

Step1: Calculate net increase

The number of mice born is 1000 and the number of mice that die is 200. The net increase in the number of mice is $1000 - 200=800$.

Step2: Calculate per - capita growth rate

The per - capita growth rate ($r$) is calculated by the formula $r=\frac{\text{Net increase}}{\text{Initial population}}$. The initial population is 2000. So $r = \frac{800}{2000}=0.4$.

Step1: Determine number of doubling periods

The doubling time is 12 years and the time period is 36 years. The number of doubling periods $n=\frac{36}{12}=3$.

Step2: Calculate final population

The initial population $P_0 = 300$. The population after $n$ doubling periods is given by $P = P_0\times2^n$. Substituting the values, we get $P=300\times2^3=300\times8 = 2400$.

Step1: Calculate number of deaths

The number of fish in year 2 is 36 and in year 3 is 22. The number of deaths $d=36 - 22 = 14$.

Step2: Calculate mortality rate

The mortality rate ($m$) is calculated by the formula $m=\frac{\text{Number of deaths}}{\text{Initial number (at start of the time - interval)}}$. The initial number at the start of the time - interval (year 2) is 36. So $m=\frac{14}{36}\approx0.39$.

Answer:

$0.4$

11.