Question

extend the table.
the table shows the actual day 4 values.
lets settle the day 10 question by extending the table.
enter values for days 5 - 10.
when youre done, continue to the next screen.
day 1 2 3 4 5 6 7 8 9 10
avis rule (dollars) 0.01 0.02 0.04 0.08
benitas rule (dollars) 100 200 300 400

Explanation:

Step1: Analyze Avi's Rule pattern

Looking at Avi's Rule values: Day 1: \(0.01\), Day 2: \(0.02\), Day 3: \(0.04\), Day 4: \(0.08\). We can see that each day the value is doubling (geometric sequence with common ratio \(r = 2\)). So the formula for Avi's Rule on day \(n\) is \(a_n=0.01\times2^{n - 1}\) (since on day 1, \(n = 1\), \(0.01\times2^{0}=0.01\)).

Step2: Analyze Benita's Rule pattern

Looking at Benita's Rule values: Day 1: \(100\), Day 2: \(200\), Day 3: \(300\), Day 4: \(400\). We can see that each day the value is increasing by \(100\) (arithmetic sequence with common difference \(d = 100\)). So the formula for Benita's Rule on day \(n\) is \(b_n=100+(n - 1)\times100=100n\) (since on day 1, \(n = 1\), \(100\times1 = 100\)).

Step3: Calculate values for Day 5 - Day 10 for Avi's Rule

• Day 5: \(a_5=0.01\times2^{5 - 1}=0.01\times16 = 0.16\)
• Day 6: \(a_6=0.01\times2^{6 - 1}=0.01\times32 = 0.32\)
• Day 7: \(a_7=0.01\times2^{7 - 1}=0.01\times64 = 0.64\)
• Day 8: \(a_8=0.01\times2^{8 - 1}=0.01\times128 = 1.28\)
• Day 9: \(a_9=0.01\times2^{9 - 1}=0.01\times256 = 2.56\)
• Day 10: \(a_{10}=0.01\times2^{10 - 1}=0.01\times512 = 5.12\)

Step4: Calculate values for Day 5 - Day 10 for Benita's Rule

• Day 5: \(b_5=100\times5 = 500\)
• Day 6: \(b_6=100\times6 = 600\)
• Day 7: \(b_7=100\times7 = 700\)
• Day 8: \(b_8=100\times8 = 800\)
• Day 9: \(b_9=100\times9 = 900\)
• Day 10: \(b_{10}=100\times10 = 1000\)

Day	Avi's Rule (Dollars)	Benita's Rule (Dollars)
2	\(0.02\)	\(200\)
3	\(0.04\)	\(300\)
4	\(0.08\)	\(400\)
5	\(0.16\)	\(500\)
6	\(0.32\)	\(600\)
7	\(0.64\)	\(700\)
8	\(1.28\)	\(800\)
9	\(2.56\)	\(900\)
10	\(5.12\)	\(1000\)

Answer:

The extended table is as shown above with Avi's Rule and Benita's Rule values calculated for days 5 - 10 using the identified patterns (geometric sequence for Avi, arithmetic sequence for Benita).