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(d) Using DESMOS, graph the function y = W(t) (including the asymptote) until the end of day 7. Use the viewing window: -0.5

(d) Using DESMOS, graph the function y = W(t) (including the asymptote) until the end of day 7. Use the viewing window: -0.5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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only part (d), (e), (f).

3. For this question, a = 100(n1 + n4) where ni is the first digit of your student number and n4 is the fourth digit of your student number. For Halloween, Ambrosia collected a bag of candy. Ambrosia weighed her bag and found that there were a grams of candy in total. Ambrosia ate half her candy on the first day (the day after Halloween). Her father told her that if she continued to eat it at that rate the candy would only last one more day, so Ambrosia decided that each day she would only eat half of the weight of the candy left in the bag. She hypothesised that this would allow her to eat candy every day and never run out. Ambrosia decided it might be useful to use Mathematics to think about her remaining candy. She assigns t and W such that • t is a variable representing the number of days since Halloween. W (t) represents the weight (in grams) of the remaining candy at the end of the day t. To understand what would be an appropriate mathematical model for this problem Ambrosia starts by making a table. (a) Continue the table of values of t, W(t), below. Include values for the seven days after Halloween. t 1 2 ... W (t) (b) Now suppose that Ambrosia chooses to model the weight of the candy left in the bag at the end each day using a decreasing exponential function of the form W (t) = Ba-t. Determine the values of B and a for this model. Determine a suitable domain for the function W, based on the situation being modelled. Justify your choice of domain. (c) According to the model in (b), what is the weight of the remaining candy Ambrosia has at the end of day 10? Write your answer to the nearest whole gram. (d) Using DESMOS, graph the function y = W(t) (including the asymptote) until the end of day 7. Use the viewing window: -0.5 <t < 8 and –59 < y < 1900. (e) According to your model, will Ambrosia's candy last forever? Justify your answer. (f) Comment on whether you think this model is realistic.
Transcribed Image Text:3. For this question, a = 100(n1 + n4) where ni is the first digit of your student number and n4 is the fourth digit of your student number. For Halloween, Ambrosia collected a bag of candy. Ambrosia weighed her bag and found that there were a grams of candy in total. Ambrosia ate half her candy on the first day (the day after Halloween). Her father told her that if she continued to eat it at that rate the candy would only last one more day, so Ambrosia decided that each day she would only eat half of the weight of the candy left in the bag. She hypothesised that this would allow her to eat candy every day and never run out. Ambrosia decided it might be useful to use Mathematics to think about her remaining candy. She assigns t and W such that • t is a variable representing the number of days since Halloween. W (t) represents the weight (in grams) of the remaining candy at the end of the day t. To understand what would be an appropriate mathematical model for this problem Ambrosia starts by making a table. (a) Continue the table of values of t, W(t), below. Include values for the seven days after Halloween. t 1 2 ... W (t) (b) Now suppose that Ambrosia chooses to model the weight of the candy left in the bag at the end each day using a decreasing exponential function of the form W (t) = Ba-t. Determine the values of B and a for this model. Determine a suitable domain for the function W, based on the situation being modelled. Justify your choice of domain. (c) According to the model in (b), what is the weight of the remaining candy Ambrosia has at the end of day 10? Write your answer to the nearest whole gram. (d) Using DESMOS, graph the function y = W(t) (including the asymptote) until the end of day 7. Use the viewing window: -0.5 <t < 8 and –59 < y < 1900. (e) According to your model, will Ambrosia's candy last forever? Justify your answer. (f) Comment on whether you think this model is realistic.
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