Section C Section C Checkpoint

Problem 1

A group of 10 students form a Good Deed Club. Their mission is to each perform a good deed for 3 people on a day, convince those 3 people to perform good deeds for 3 other people each, and continue the process. Assume that everyone in the chain does their part.
  1. Let the number of days be the independent variable and the number of good deeds done caused by this chain be the dependent variable. Is the relationship a function? Explain your reasoning.
  2. Write a function that represents this relationship.
Show Solution
Solution
  1. Yes, because each day there is a certain number of good deeds done that were caused by this chain.
  2. G(t)=10⋅3tG(t) = 10 \boldcdot 3^t
Show Sample Response
Sample Response
  1. Yes, because each day there is a certain number of good deeds done that were caused by this chain.
  2. G(t)=10⋅3tG(t) = 10 \boldcdot 3^t

Problem 2

Match the function to the graph that represents the function. Explain your reasoning for each.

  1. f(t)=2⋅3tf(t) = 2 \boldcdot 3^t

  2. g(t)=2⋅(1.5)tg(t) = 2 \boldcdot (1.5)^t

  3. h(t)=3⋅(32)th(t) = 3 \boldcdot \left( \frac{3}{2} \right)^t

  4. j(t)=3⋅(23)tj(t) = 3 \boldcdot \left( \frac{2}{3} \right)^t

graph of 4 exponential functions labeled A, B, C, and D

Show Solution
Solution
  1. A. Sample reasoning: It goes through the point (0,2)(0,2), is the steepest, and has the greatest growth factor.
  2. C. Sample reasoning: It goes through the point (0,2)(0,2), but grows slower than the graph for f(t)f(t).
  3. B. Sample reasoning: It goes through the point (0,3)(0,3) and shows exponential growth because the growth factor is greater than 1.
  4. D. Sample reasoning: It goes through the point (0,3)(0,3) and shows exponential decay because the growth factor is between 0 and 1.
Show Sample Response
Sample Response
  1. A. Sample reasoning: It goes through the point (0,2)(0,2), is the steepest, and has the greatest growth factor.
  2. C. Sample reasoning: It goes through the point (0,2)(0,2), but grows slower than the graph for f(t)f(t).
  3. B. Sample reasoning: It goes through the point (0,3)(0,3) and shows exponential growth because the growth factor is greater than 1.
  4. D. Sample reasoning: It goes through the point (0,3)(0,3) and shows exponential decay because the growth factor is between 0 and 1.