Basic Calculus Poformance Task 4 INCLUSIVE TOPICS Related Rates CONTENT STANDARD PERFORMANCE STAN...
Basic Calculus Poformance Task 4 INCLUSIVE TOPICS Related Rates CONTENT STANDARD PERFORMANCE STANDARD The lcarncrs demonstrate the understanding of the basic concepts of derivatives. The lcarners shall be able to formulatc and solve accurately situational problems involving related rates. You are a computational biologist doing a research on oriental fruit moth and pomelo fruits. The oriental fruit moth is an insect that causes serious damage to pomelo fruits. Adult fruit moths emerge from cocoons and they soon mate. The female lays as many as 30-60 eggs on the leaves of pomelo trees. After the fruit moth larva hatches from its egg, it goes looking for pomelo. The time between hatching and findin pomelo is called the searching period. Once a fruit moth finds a pomelo, it squirms into the fruit and eats the fruit and seeds of the fruit, thereby ruining it. After about 4 weeks, the oriental fruit moth backs out of the pomelo and crawls under the bark under the bark of the tree or into the soil where it forms a cocoon. Observations regarding the behavior of oriental fruit moths indicate that the length of the searching period S(T), and the percentage of larvae that survive the searching period, N(T), depend on the air temperature, T. Methods of data analysis (polynomial regression) applied to data recorded from observations suggest that if T is mcasured in degrees Celsius, where Tis from 20 to 30, then S(T) and N(T) may be modeled by and S(T)(aT + bT-c)-1 days N(T)0.8572 + 45.4T+ d (Please refer to the values of a, b, c, and d assigned to your pair/group.) Using these formulas, you are tasked to answer the following questions. 1. What do these formulas for S(T) and N(T) predict for the length of searching period and percentage of larvae surviving the scarching period when the air temperature is 25 degrees Celsius? 2. Find ds/dI, the rate of change of the searching period with respect to temperature T When does this rate equal to zero? What (if anything) occurs when dS/dT 0? TASK 3. Find dN/ds, the rate of change of the perccntage of larvac surviving the scarching period with respect to the length of the scarching period using the chain rule, dN/dT(dN/ds) (ds/dT) What (if any) information does this provide? In addition to the questions above, you also need to answer the following problem. To cstimatc the amount of wood in the trunk of a pomclo trcc, it is rcasonable to assume that the trunk is a cutoff cone. If the upper radius of the trunk is r, the lower radius is R, and the height is H, the volume of the wood is given by VH (R+ rR+ r)/3 Suppose r, R, and H are increasing at the respective rates of 4 in/yr, 5 in/yr, and 9 in incrcasing at the time when2 fcct, R 3 fect, and H 5 fect? Working in groups of 2-3 members, you need to prepare an initial report using one sheet of a long size (8.5" x 13") paper in presenting the details of the solution to each item. For each s a. include the variables used and their representations b. provide detailed computation c. interpret the result of the computation bond Your output will be evaluated based on the rubric provided bel
Basic Calculus Poformance Task 4 INCLUSIVE TOPICS Related Rates CONTENT STANDARD PERFORMANCE STANDARD The lcarncrs demonstrate the understanding of the basic concepts of derivatives. The lcarners shall be able to formulatc and solve accurately situational problems involving related rates. You are a computational biologist doing a research on oriental fruit moth and pomelo fruits. The oriental fruit moth is an insect that causes serious damage to pomelo fruits. Adult fruit moths emerge from cocoons and they soon mate. The female lays as many as 30-60 eggs on the leaves of pomelo trees. After the fruit moth larva hatches from its egg, it goes looking for pomelo. The time between hatching and findin pomelo is called the searching period. Once a fruit moth finds a pomelo, it squirms into the fruit and eats the fruit and seeds of the fruit, thereby ruining it. After about 4 weeks, the oriental fruit moth backs out of the pomelo and crawls under the bark under the bark of the tree or into the soil where it forms a cocoon. Observations regarding the behavior of oriental fruit moths indicate that the length of the searching period S(T), and the percentage of larvae that survive the searching period, N(T), depend on the air temperature, T. Methods of data analysis (polynomial regression) applied to data recorded from observations suggest that if T is mcasured in degrees Celsius, where Tis from 20 to 30, then S(T) and N(T) may be modeled by and S(T)(aT + bT-c)-1 days N(T)0.8572 + 45.4T+ d (Please refer to the values of a, b, c, and d assigned to your pair/group.) Using these formulas, you are tasked to answer the following questions. 1. What do these formulas for S(T) and N(T) predict for the length of searching period and percentage of larvae surviving the scarching period when the air temperature is 25 degrees Celsius? 2. Find ds/dI, the rate of change of the searching period with respect to temperature T When does this rate equal to zero? What (if anything) occurs when dS/dT 0? TASK 3. Find dN/ds, the rate of change of the perccntage of larvac surviving the scarching period with respect to the length of the scarching period using the chain rule, dN/dT(dN/ds) (ds/dT) What (if any) information does this provide? In addition to the questions above, you also need to answer the following problem. To cstimatc the amount of wood in the trunk of a pomclo trcc, it is rcasonable to assume that the trunk is a cutoff cone. If the upper radius of the trunk is r, the lower radius is R, and the height is H, the volume of the wood is given by VH (R+ rR+ r)/3 Suppose r, R, and H are increasing at the respective rates of 4 in/yr, 5 in/yr, and 9 in incrcasing at the time when2 fcct, R 3 fect, and H 5 fect? Working in groups of 2-3 members, you need to prepare an initial report using one sheet of a long size (8.5" x 13") paper in presenting the details of the solution to each item. For each s a. include the variables used and their representations b. provide detailed computation c. interpret the result of the computation bond Your output will be evaluated based on the rubric provided bel