For this question, a = 100(nı + 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. 1 2... W (t) | a ... (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.
For this question, a = 100(nı + 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. 1 2... W (t) | a ... (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.
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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Transcribed Image Text:3. For this question, a =
100(n1 + n4) where n1 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.
|0 1
t
2
W (t) | a
...
(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.
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