Shortcut Methods and Tricks for Numerical Problems

Photosynthesis:

• Use the Lambert-Beer law to calculate the light intensity absorbed by a leaf at different wavelengths:

$$I = I_0 e^{-\varepsilon C l}$$

where (I) is the intensity of the light after passing through the leaf, (I_0) is the intensity of the incident light, (\epsilon) is the extinction coefficient of the leaf, (C) is the concentration of chlorophyll in the leaf, and (l) is the path length of the light through the leaf.

• Use the Michaelis-Menten equation to calculate the rate of photosynthesis as a function of CO2 concentration:

$$V = \frac{V_{max} [CO_2]}{K_m + [CO_2]}$$

where (V) is the rate of photosynthesis, (V_{max}) is the maximum rate of photosynthesis, (K_m) is the Michaelis-Menten constant, and ([CO_2]) is the CO2 concentration.

• Use the Arrhenius equation to calculate the rate of photosynthesis as a function of temperature:

$$k = Ae^{−Ea/RT}$$

where (k) is the rate constant for photosynthesis, (A) is the pre-exponential factor, (Ea) is the activation energy, (R) is the ideal gas constant, and (T) is the temperature.

Plant Water Relations:

• Use the Poiseuille equation to calculate the rate of water flow through a plant stem: $$Q = \frac{\pi r^4 \Delta P}{8 \eta l}$$ where (Q) is the rate of flow, (r) is the radius of the stem, (\Delta P) is the pressure difference between the two ends of the stem, (\eta) is the viscosity of water, and (l) is the length of the stem.

• Use the Ohm’s law to calculate the water potential of a plant cell or tissue:

$$\Psi_w=\Psi_s-\Psi_p$$ where (\Psi_w) is the water potential, (\Psi_s) is the solute potential, and (\Psi_p) is the pressure potential.

Plant Growth

• Use the logarithmic equation to calculate the relative growth rate of a plant: $$RGR = \frac{\ln W_2 - \ln W_1}{t_2 - t_1}$$ where (RGR) is the relative growth rate, (W_1) and (W_2) are the initial and final masses of the plant, and (t_1) and (t_2) are the initial and final times.

• Use the Mitscherlich equation to calculate the growth of a plant as a function of nutrient concentration: $$W=A(1-e^{-C}$$ where (W) is the weight of the plant, (A) is maximum weight, (C) is a constant and (X) is the amount of nutrient present.

Plant Responses:

• Use the phototropic response equation to calculate the angle of bending of a plant stem towards a light source:

$$ \theta = \frac{I_{light1}-I_{light2}}{I_{light1}$$ where (\theta) is the angle of bending, and (I_{light1}) and (I_{light2}) refer to the intensities of light received by the two sides of the stem.

• Use the geotropic response equation to calculate the angle of bending of a plant root in response to gravity: $$ \theta = \frac{g t^2}{L}$$ where (g) is the acceleration due to gravity, (t) is the time, and (L) is the length of the organ responding.

Plant Tissue Culture:

• Use the plant regeneration efficiency equation to determine the efficiency of regeneration from different types of explants: $$Plant \ regeneration \ efficiency=\frac{Number \ of \ plants \ developed}{Number \ of \ explants \ cultured} \times 100$$

Plant Breeding:

• Use the selection differential equation to calculate the difference between the mean of a selected population and the mean of the original population: $$ S = \overline X - \mu $$ where (S) is the selection differential, ( \overline X) is the mean of the selected population and ( \mu) is the mean of the original population.

Plant Ecology:

• Use the Simpson’s diversity index equation to calculate the diversity of a plant community: $$Simpson’s \ diversity \ index (D) = 1 - \frac{\sum n(n-1)}{N(N-1)}$$ where (N) is the total number of individuals and (n) is the number of individuals in each species

• Use the Shannon-Wiener index equation to calculate the diversity of a plant community: $$ H’= -\sum (Pi \times ln Pi) $$ Where ( Pi ) is the proportion of individuals of species (i) in the sample, and In is the natural logarithm.