al Metro by T-Mobile 12:57 PM @ 1 1 95% Document (23) B Q E . . . Group of students from GGC and Kamphaeng Phet Rajabat collected data for a scientific experiment. The data collection was based on the following experiment: "5 sets of bowls (Yellow, Blue and White) where set up 10 meters apart, starting at a flower patch and extended for 40 meters," a) Based on the data at what bowl set do you expect to have the maximum number of Spiders? Why ? The picture below give a visual representation of the problem: 00 00 10 20 30 40 b) Can we approximate the number of spiders in each bowl set by using the information above? Why or why not? After several weeks of collecting, the data was compiled and stored in excel tables. Unfortunately, one of the GGC students fell asleep over the computer and erased most of the data pressing the keyboard with his nose. Fortunately, enough data survived to (approximately) recover most of the lost data points. Use calculus eeded to solve the following prob c) At some point, one of the students who worked on the collection of the data remembered Problem 1: [Linear Approximation] that there were 60 spiders in Bowl Set 3. Using the information, calculate and write the number of Spiders in each set and the total number of spiders for all sets. the following data survived for the Yellow Bowl set: Rate of Sample change of the Site Number of Bees per BEES in the meter trap (dB/dm) Yellow 1 10 0.4 Problem 3: [Optimization part 2) Yellow 2 The following chart represent the rate of change for the pollinators that got into the traps. Yellow3 Yellow 4 Yellow 5 Rate of chage of the Pollinators per meter (Set to Set) Change S Set 1 to 2 Change fram Bowl set 2 to 3 Change set 3 10 4 Change It pain Set 3 to 4 -0.3 -0.9 -1.2 -15 a) Based on the information of the table, was the number of Bees increasing or decreasing as we move away from Yellow towards Yellow 2? By how much per meter? By how much per 10 meters? [Explain!] 27 For all of the following problems recall that any two neighboring bowl sets is 10 meters. by Use the data from the table to find linear equation B(m) where m is the number of meters from the first yellow bowl and B is the number of bees at position m. (Show work! Hint: a) Find the area of the first rectangle. What does the area represent? B(0)-101 c) Use your equation from part b) to predict how many Bees should we expect to be captured in a hypothetical trap placed 5 m away from Yellow 1? b) Find the area of the third rectangle. What does the area represent? ) Based on the data at what bowl set do you expect to have the maximum number of d) Use your equation from part b) to fill the table above [Hint: Keep in mind that no parts of a bee pollinators? Why? can be found in the bowls] Problem 2: [Optimization] d) If we know that there were 100 pollinators is Bow 1, calculate how many were in Bow 3 and Bow 5. The following table represented the number of Spiders per bowl sets. Rate of change of of the Spiders SPIDERS per meter to Set) Bowl Set 1 3.8 Bowl Set 2 1.2 e) Approximate using the data the number of pollinators expected to be catch at the following Bowl Set 3 -2.7 distances: -0.9 1) 5 m away from Bow set 1; 2) 15 m away from Set 1. Bowl Set 4 Bowl Set 5 CO
