Q: A solution contains 0.2 M NaCl at 25°C. Calculate the solute potential ($$\psi_s) $$using $$\psi_s = -iCRT$$, where $$i = 2$$ for NaCl, $$C = 0.2$$, $$R = 0.0831$$, and $$T = 25 + 273.$$

$$\psi_s = -2 \times 0.2 \times 0.0831 \times 298 = -9.91$$ bars

Q: If the probability of event A is 0.3 and the probability of event B is 0.5, and they are independent, what is the probability that both A and B occur?

$$P(A \text{ and } B) = P(A) \times P(B) = 0.3 \times 0.5 = 0.15$$

Q: In a population, the frequency of allele A ($$p) is 0.7 $$and allele a ($$q) is 0.3. $$According to Hardy-Weinberg equilibrium, what is the expected frequency of heterozygotes?

$$2pq = 2 \times 0.7 \times 0.3 = 0.42$$

Q: A population of bacteria grows exponentially with $$r_{max} = 0.5$$ per hour and an initial population size $$N = 100. $$What is the rate of change in population size ($$\frac{dN}{dt}) $$after 1 hour?

$$\frac{dN}{dt} = r_{max} N = 0.5 \times 100 = 50$$

Q: A population of rabbits has a carrying capacity ($$K) of 500$$, a current population size ($$N) of 200$$, and $$r_{max} = 0.2. $$What is the rate of change in population size ($$\frac{dN}{dt}) $$using the logistic growth equation?

$$\frac{dN}{dt} = r_{max} N \left( \frac{K-N}{K} \right ) = 0.2 \times 200 \left( \frac{500-200}{500} \right ) = 0.2 \times 200 \times 0.6 = 24$$

Q: A cube-shaped cell has a side length of 10 μm. What is its surface area-to-volume ratio?

Surface area $$= 6s^2$ = 6 \times 10^2$ = 600$$ μm$$^2$$, Volume $$= s^3$ = 10^3$ = 1000$$ μm$$^3$$, Ratio $$= \frac{600}{1000} = 0.6$$

Question 1

A cell is shaped like a sphere with a radius of 5 μm. What is the surface area-to-volume ratio of this cell? Use the equations $$V = \frac{4}{3}\pi r^3$ and SA = 4$$\pi $$r^2.$$

Accepted Answer

The ratio is $$\frac{4\pi r^2$}{\frac{4}{3}\pi r^3$} = \frac{3}{r}$$, so for $$r = 5$$, the ratio is $$0.6$$

Question 2

A plant cell is placed in a solution with a solute potential ($$\psi_s) of$$ $$-0.5$$ bars and a pressure potential ($$\psi_p) of$$ $$1.2$$ bars. What is the water potential ($$\psi) of $$the cell?

Accepted Answer

$$\psi = \psi_p + \psi_s = 1.2 + (-0.5) = 0.7$$ bars

Question 3

A solution contains 0.2 M NaCl at 25°C. Calculate the solute potential ($$\psi_s) $$using $$\psi_s = -iCRT$$, where $$i = 2$$ for NaCl, $$C = 0.2$$, $$R = 0.0831$$, and $$T = 25 + 273.$$

Accepted Answer

$$\psi_s = -2 	imes 0.2 	imes 0.0831 	imes 298 = -9.91$$ bars

Question 4

If the probability of event A is 0.3 and the probability of event B is 0.5, and they are independent, what is the probability that both A and B occur?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B) = 0.3 	imes 0.5 = 0.15$$

Question 5

In a population, the frequency of allele A ($$p) is 0.7 $$and allele a ($$q) is 0.3. $$According to Hardy-Weinberg equilibrium, what is the expected frequency of heterozygotes?

Accepted Answer

$$2pq = 2 	imes 0.7 	imes 0.3 = 0.42$$

Question 6

A population of bacteria grows exponentially with $$r_{max} = 0.5$$ per hour and an initial population size $$N = 100. $$What is the rate of change in population size ($$\frac{dN}{dt}) $$after 1 hour?

Accepted Answer

$$\frac{dN}{dt} = r_{max} N = 0.5 	imes 100 = 50$$

Question 7

A population of rabbits has a carrying capacity ($$K) of 500$$, a current population size ($$N) of 200$$, and $$r_{max} = 0.2. $$What is the rate of change in population size ($$\frac{dN}{dt}) $$using the logistic growth equation?

Accepted Answer

$$\frac{dN}{dt} = r_{max} N \left( \frac{K-N}{K} ight ) = 0.2 	imes 200 \left( \frac{500-200}{500} ight ) = 0.2 	imes 200 	imes 0.6 = 24$$

Question 8

In a community, there are 3 species: A (20 individuals), B (30 individuals), and C (50 individuals). What is the Simpson's Diversity Index for this community?

Accepted Answer

Total $$N = 20 + 30 + 50 = 100. $$Diversity Index $$= 1 - \sum \left( \frac{n}{N} \right )^2$ = 1 - \left( \frac{20}{100} \right )^2$ - \left( \frac{30}{100} \right )^2$ - \left( \frac{50}{100} \right )^2$ = 1 - (0.04 + 0.09 + 0.25) = 1 - 0.38 = 0.62$$

Question 9

A cube-shaped cell has a side length of 10 μm. What is its surface area-to-volume ratio?

Accepted Answer

Surface area $$= 6s^2$ = 6 	imes 10^2$ = 600$$ μm$$^2$$, Volume $$= s^3$ = 10^3$ = 1000$$ μm$$^3$$, Ratio $$= \frac{600}{1000} = 0.6$$

Question 10

If a population has a birth rate ($$B) of 40 $$per year and a death rate ($$D) of 25 $$per year, what is the change in population size per year ($$\frac{dN}{dt}$$)?

Accepted Answer

$$\frac{dN}{dt} = B - D = 40 - 25 = 15$$

Question 11

A plant cell is placed in a solution with a solute potential ($$\psi_s) of$$ $$-1.0$$ bars and a pressure potential ($$\psi_p) of$$ $$0.5$$ bars. What will happen to the cell?

Accepted Answer

Water will move out of the cell because $$\psi is $$negative, causing plasmolysis.

Question 12

If the frequency of allele A ($$p) in a $$population is 0.4, what is the frequency of allele a ($$q$$)?

Accepted Answer

$$q = 1 - p = 1 - 0.4 = 0.6$$

Question 13

A population of fish is observed to have a maximum per capita growth rate ($$r_{max}) of 0.1 $$per month and a current population size ($$N) of 1000. $$What is the expected change in population size per month ($$\frac{dN}{dt}) $$under exponential growth?

Accepted Answer

$$\frac{dN}{dt} = r_{max} N = 0.1 	imes 1000 = 100$$

Question 14

In a population, the frequency of allele A ($$p) is 0.5 $$and allele a ($$q) is 0.5. $$What is the expected frequency of homozygous recessive individuals?

Accepted Answer

$$q^2$$ = $$0.5^2 = 0.25$

Question 15

A rectangular solid cell has a length of 10 μm, width of 5 μm, and height of 2 μm. What is its surface area?

Accepted Answer

Surface area $$= 2lh + 2lw + 2wh = 2 	imes 10 	imes 2 + 2 	imes 10 	imes 5 + 2 	imes 5 	imes 2 = 40 + 100 + 20 = 160$$ μm$$^2$$

Question 16

If a population has 100 individuals and the birth rate is 0.05 per year, while the death rate is 0.02 per year, what is the change in population size per year?

Accepted Answer

$$\frac{dN}{dt} = (B - D) 	imes N = (0.05 - 0.02) 	imes 100 = 0.03 	imes 100 = 3$$

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