Section A Section A Checkpoint

Problem 1

Consider the two patterns. For each pattern: 

  1. Determine whether they grow by a constant difference, constant factor, or neither.
  2. If they grow by a constant difference or factor, find its value. Show your reasoning.

Pattern 1

xx 1 2 3 4 5
yy 8 16 32 64 128

Pattern 2

aa 0 1 2 3 4
bb 8 16 24 32 40

Show Solution
Solution
Pattern 1 
  1. It grows by a constant factor.
  2. The factor is 2 because 168=2\frac{16}{8} = 2, 3216=2\frac{32}{16}=2, and so on.
Pattern 2
  1. It grows by a constant difference.
  2. The difference is 8 because 16−8=816 - 8 = 8, 24−16=824-16=8, and so on.
Show Sample Response
Sample Response
Pattern 1 
  1. It grows by a constant factor.
  2. The factor is 2 because 168=2\frac{16}{8} = 2, 3216=2\frac{32}{16}=2, and so on.
Pattern 2
  1. It grows by a constant difference.
  2. The difference is 8 because 16−8=816 - 8 = 8, 24−16=824-16=8, and so on.

Problem 2

You are given 2 options for claiming prize money that must not be touched until you are a certain age. 

  • Option 1: You are given $50,000 every year. 
  • Option 2: You are given $10,000 initially, and its value is doubled every year.

Will Option 2 ever be worth more than Option 1? Show your reasoning.

Show Solution
Solution
Yes. Sample response: After 5 years, Option 1 will be worth $250,000 (50,000⋅5=250,00050,000 \boldcdot 5 = 250,000), and Option 2 will be worth $320,000 (10,000⋅25=320,00010,000 \boldcdot 2^5 = 320,000).
Show Sample Response
Sample Response
Yes. Sample response: After 5 years, Option 1 will be worth $250,000 (50,000⋅5=250,00050,000 \boldcdot 5 = 250,000), and Option 2 will be worth $320,000 (10,000⋅25=320,00010,000 \boldcdot 2^5 = 320,000).