8. suppose that of a cohort of 200 rats in a rat colony born in january, 160 are still alive at the start of march and 120 are still alive at the start of may.
a. what is the survivorship up to the start of march? round to the nearest hundredth.
b. what is the mortality rate from the beginning of march to the beginning of may? round to the nearest hundredth.
c. if the survivorship during may is 0.3, how many rats died during the month of may? round to the nearest whole number.

9. suppose that of a cohort of 150 mice in a mouse colony born in february, 125 are still alive in march and 115 are still alive in april.
a. what is the survivorship up to the start of april? round to the nearest hundredth.
b. what is the mortality rate during the month of march? round to the nearest hundredth.
c. if the survivorship during april is 0.5, how many mice will there be at the start of may? round to the nearest whole number.

10. 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.

11. 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?

12. 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.

13. 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 |
| --- | --- | --- |
| initial # of plants | 500 | 300 |
| 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 |
| --- | --- | --- |
| b (births during time interval) | | |
| d (deaths during time interval) | | |
| b (per capita birth rate) | | |
| d (per capita death rate) | | |
| r (per capita rate of increase) | | |

Question

8. suppose that of a cohort of 200 rats in a rat colony born in january, 160 are still alive at the start of march and 120 are still alive at the start of may.
a. what is the survivorship up to the start of march? round to the nearest hundredth.
b. what is the mortality rate from the beginning of march to the beginning of may? round to the nearest hundredth.
c. if the survivorship during may is 0.3, how many rats died during the month of may? round to the nearest whole number.

9. suppose that of a cohort of 150 mice in a mouse colony born in february, 125 are still alive in march and 115 are still alive in april.
a. what is the survivorship up to the start of april? round to the nearest hundredth.
b. what is the mortality rate during the month of march? round to the nearest hundredth.
c. if the survivorship during april is 0.5, how many mice will there be at the start of may? round to the nearest whole number.

10. 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.

11. 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?

12. 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.

13. 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 |
| --- | --- | --- |
| initial # of plants | 500 | 300 |
| 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 |
| --- | --- | --- |
| b (births during time interval) |  |  |
| d (deaths during time interval) |  |  |
| b (per capita birth rate) |  |  |
| d (per capita death rate) |  |  |
| r (per capita rate of increase) |  |  |

Accepted Answer

### Question 8a
# Explanation:
## Step1: Recall survivorship formula
Survivorship ($l$) is the number of survivors divided by the initial number. Formula: $l=\frac{\text{Number of survivors}}{\text{Initial number}}$
Initial number of rats = 200, Survivors at start of March = 160.
## Step2: Calculate survivorship
$l = \frac{160}{200}=0.80$
# Answer:
0.80

### Question 8b
# Explanation:
## Step1: Find number of deaths between March and May
Survivors at start of March = 160, Survivors at start of May = 120. Deaths = 160 - 120 = 40.
## Step2: Recall mortality rate formula
Mortality rate ($m$) is deaths divided by initial number for the period. Here, initial for the period is survivors at start of March. Formula: $m=\frac{\text{Deaths}}{\text{Survivors at start of period}}$
## Step3: Calculate mortality rate
$m=\frac{40}{160}=0.25$
# Answer:
0.25

### Question 8c
# Explanation:
## Step1: Recall survivorship and deaths relation
Survivorship ($l$) = $\frac{\text{Survivors at end}}{\text{Survivors at start}}$, so Survivors at end = $l\times\text{Survivors at start}$. Deaths = Survivors at start - Survivors at end.
Survivors at start of May = 120, $l = 0.3$.
## Step2: Calculate survivors at end of May
Survivors at end = $0.3\times120 = 36$
## Step3: Calculate deaths
Deaths = 120 - 36 = 84
# Answer:
84

### Question 9a
# Explanation:
## Step1: Recall survivorship formula
$l=\frac{\text{Number of survivors}}{\text{Initial number}}$
Initial number of mice = 150, Survivors at start of April = 115.
## Step2: Calculate survivorship
$l=\frac{115}{150}\approx0.77$ (rounded to nearest hundredth)
# Answer:
0.77

### Question 9b
# Explanation:
## Step1: Find number of deaths in March
Survivors at start of March (initial for March) = 125? Wait, no: Initial cohort in February = 150, survivors in March = 125. So deaths in March = 150 - 125 = 25. Wait, no: Mortality rate during March: initial number for March is 150? Wait, no: Cohort born in February (initial = 150), survivors in March = 125. So deaths during March: 150 - 125 = 25. Mortality rate is deaths divided by initial number (for the period, which is February to March, so initial is 150? Wait, no: Mortality rate during March: the population at start of March is 125? Wait, no, the cohort is born in February, so initial size $N_0 = 150$ (February), $N_1 = 125$ (March), $N_2 = 115$ (April). Mortality rate during March (from Feb to March? No, during March: from start of March to start of April? Wait, the question says "mortality rate during the month of March". So start of March: 125 mice, end of March (start of April): 115. Wait, no: "of a cohort of 150 mice in a mouse colony born in February, 125 are still alive in March and 115 are still alive in April." So March is the month after February, so during March (from February end to March end? Wait, the cohort is born in February, so initial (Feb) = 150, March: 125, April: 115. So mortality rate during March: deaths in March / initial in March. Initial in March is 125? No, mortality rate is (deaths) / (initial population at start of period). The period is March, so start of March: 125? Wait, no, the cohort is 150 (Feb), so in March, the number alive is 125 (so deaths from Feb to March: 25), then from March to April: deaths are 125 - 115 = 10. Wait, the question is "mortality rate during the month of March". So the period is March, so the population at start of March is 125? No, the cohort is born in February, so the initial population for the cohort is 150 (Feb). Then, during March (the month), the number alive goes from 125 (start of March) to 115 (start of April). Wait, maybe the problem considers the cohort's mortality during March: so start of March: 125, end of March: 115. So deaths = 125 - 115 = 10. Mortality rate = deaths / start of period population = 10 / 125 = 0.08? Wait, no, maybe I messed up. Wait, the cohort is 150 (Feb), alive in March: 125 (so deaths from Feb to March: 25), then alive in April: 115 (deaths from March to April: 10). The question is "mortality rate during the month of March" – so the period is March, so the population at the start of March is 125, and at the end of March is 115. So mortality rate is (125 - 115)/125 = 10/125 = 0.08? Wait, but let's check the formula. Mortality rate is usually (number of deaths) / (number at risk at start of period). So start of March: 125, deaths: 10, so 10/125 = 0.08. Wait, but maybe the initial cohort is 150, so during March, the number at start is 125. So yes, 10/125 = 0.08. Wait, but let's recalculate: 125 - 115 = 10. 10 / 125 = 0.08. So mortality rate is 0.08.
Wait, no, maybe the problem is considering the cohort's mortality from birth (Feb) to March: no, the question is "during the month of March". So start of March: 125, end of March: 115. So deaths: 10. Mortality rate: 10 / 125 = 0.08.
## Step1: Find deaths in March
Survivors at start of March: 125, Survivors at start of April: 115. Deaths = 125 - 115 = 10.
## Step2: Calculate mortality rate
Mortality rate = $\frac{\text{Deaths}}{\text{Survivors at start of March}}=\frac{10}{125}=0.08$
# Answer:
0.08

### Question 9c
# Explanation:
## Step1: Recall survivorship and survivors relation
Survivorship ($l$) = $\frac{\text{Survivors at end}}{\text{Survivors at start}}$, so Survivors at end = $l\times\text{Survivors at start}$.
Survivors at start of April = 115, $l = 0.5$.
## Step2: Calculate survivors at start of May
Survivors at end = $0.5\times115 = 57.5\approx58$ (rounded to nearest whole number)
# Answer:
58

### Question 10
# Explanation:
## Step1: Recall per capita growth rate formula
Per capita growth rate ($r$) = $\frac{\text{Change in population}}{\text{Initial population}}$. Change in population = births - deaths.
Initial population ($N$) = 2000, Births ($B$) = 1000, Deaths ($D$) = 200.
## Step2: Calculate change in population
$\Delta N = B - D = 1000 - 200 = 800$
## Step3: Calculate per capita growth rate
$r=\frac{\Delta N}{N}=\frac{800}{2000}=0.4$
# Answer:
0.4

### Question 11
# Explanation:
## Step1: Determine number of doubling times
Doubling time ($t_d$) = 12 years, Total time ($t$) = 36 years. Number of doubling times ($n$) = $\frac{t}{t_d}=\frac{36}{12}=3$
## Step2: Recall population growth with doubling time
Population after $n$ doublings: $P = P_0\times2^n$, where $P_0$ is initial population.
$P_0 = 300$, $n = 3$.
## Step3: Calculate final population
$P = 300\times2^3 = 300\times8 = 2400$
# Answer:
2400

### Question 12
# Explanation:
## Step1: Find number of deaths between year 2 and 3
Survivors at start of year 2 (end of year 1) = 36, Survivors at start of year 3 (end of year 2) = 22. Deaths = 36 - 22 = 14.
## Step2: Recall mortality rate formula
Mortality rate ($m$) = $\frac{\text{Deaths}}{\text{Survivors at start of period}}$ (start of year 2: 36)
## Step3: Calculate mortality rate
$m=\frac{14}{36}\approx0.39$ (rounded to nearest hundredth)
# Answer:
0.39

### Question 13a
#### For Population A:
- **B (births during time interval)**: Number of new seedlings established = 100. So $B = 100$
- **D (deaths during time interval)**: Number of initial plants that die = 20. So $D = 20$
- **b (per capita birth rate)**: $b=\frac{B}{\text{Initial number of plants}}=\frac{100}{500}=0.20$
- **d (per capita death rate)**: $d=\frac{D}{\text{Initial number of plants}}=\frac{20}{500}=0.04$
- **r (per capita rate of increase)**: $r = b - d = 0.20 - 0.04 = 0.16$

#### For Population B:
- **B (births during time interval)**: Number of new seedlings established = 30. So $B = 30$
- **D (deaths during time interval)**: Number of initial plants that die = 100. So $D = 100$
- **b (per capita birth rate)**: $b=\frac{B}{\text{Initial number of plants}}=\frac{30}{300}=0.10$
- **d (per capita death rate)**: $d=\frac{D}{\text{Initial number of plants}}=\frac{100}{300}\approx0.33$ (rounded to hundredth)
- **r (per capita rate of increase)**: $r = b - d = 0.10 - 0.33 = -0.23$

# Answers (for Population A and B respectively):
- $B$: 100, 30
- $D$: 20, 100
- $b$: 0.20, 0.10
- $d$: 0.04, 0.33
- $r$: 0.16, -0.23

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QUESTION IMAGE

Question

Explanation:

Question 8a

Step1: Recall survivorship formula

Step2: Calculate survivorship

Step1: Find number of deaths between March and May

Step2: Recall mortality rate formula

Step3: Calculate mortality rate

Step1: Recall survivorship and deaths relation

Step2: Calculate survivors at end of May

Step3: Calculate deaths

Answer:

Question 8b

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

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)