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Ehsan is having a big going-out-ofbusiness sale and he wants to advertise his sale. He starts by making a large number of advertising fliers for his sale and gives 5 of his friends many fliers. He asks each of them to give fliers to 2 of their friends the next day, and to tell each of their friends to give fliers to 2 of their friends the day after, and so on. Let 
F be the number of people who will be given fliers on day 
t. Which of the following best explains the relationship between 
t and 
F ?
Choose 1 answer:
(A) The relationship is linear because the values of 
F always increase as the values of 
t increase.
(B) The relationship is exponential because 
F increases by a factor of 5 each time 
t increases by 1 .
(C) The relationship is linear because 
F increases by a factor of 5 each time 
t increases by 1 .
(D) The relationship is exponential because 
F increases by a factor of 2 each time 
t increases by 1 .

Ehsan is having a big going-out-ofbusiness sale and he wants to advertise his sale. He starts by making a large number of advertising fliers for his sale and gives 55 of his friends many fliers. He asks each of them to give fliers to 22 of their friends the next day, and to tell each of their friends to give fliers to 22 of their friends the day after, and so on. Let F F be the number of people who will be given fliers on day t t . Which of the following best explains the relationship between t t and F F ?\newlineChoose 11 answer:\newline(A) The relationship is linear because the values of F F always increase as the values of t t increase.\newline(B) The relationship is exponential because F F increases by a factor of 55 each time t t increases by 11 .\newline(C) The relationship is linear because F F increases by a factor of 55 each time t t increases by 11 .\newline(D) The relationship is exponential because F F increases by a factor of 22 each time t t increases by 11 .

Full solution

Q. Ehsan is having a big going-out-ofbusiness sale and he wants to advertise his sale. He starts by making a large number of advertising fliers for his sale and gives 55 of his friends many fliers. He asks each of them to give fliers to 22 of their friends the next day, and to tell each of their friends to give fliers to 22 of their friends the day after, and so on. Let F F be the number of people who will be given fliers on day t t . Which of the following best explains the relationship between t t and F F ?\newlineChoose 11 answer:\newline(A) The relationship is linear because the values of F F always increase as the values of t t increase.\newline(B) The relationship is exponential because F F increases by a factor of 55 each time t t increases by 11 .\newline(C) The relationship is linear because F F increases by a factor of 55 each time t t increases by 11 .\newline(D) The relationship is exponential because F F increases by a factor of 22 each time t t increases by 11 .
  1. Ehsan gives fliers: Ehsan gives 55 friends fliers on the first day. Each friend gives fliers to 22 of their friends the next day.
  2. Friends distribute fliers: On day t=1t=1, F=5F=5. On day t=2t=2, each of the 55 friends gives fliers to 22 friends, so F=5×2F=5\times2.
  3. Day t=1t=1 to t=2t=2: On day t=3t=3, each of the 5×25\times2 friends gives fliers to 22 more friends, so F=5×2×2F=5\times2\times2.
  4. Day t=2t=2 to t=3t=3: The pattern shows that each day, the number of people who receive fliers is multiplied by 22, not added by 55.
  5. Pattern of distribution: This means the relationship between tt and FF is not linear, it's exponential because the number of people doubles each day.
  6. Correct answer: The correct answer is (D) The relationship is exponential because FF increases by a factor of 22 each time tt increases by 11.

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