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 .
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 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 gives fliers: Ehsan gives 5 friends fliers on the first day. Each friend gives fliers to 2 of their friends the next day.
Friends distribute fliers: On day t=1, F=5. On day t=2, each of the 5 friends gives fliers to 2 friends, so F=5×2.
Day t=1 to t=2: On day t=3, each of the 5×2 friends gives fliers to 2 more friends, so F=5×2×2.
Day t=2 to t=3: The pattern shows that each day, the number of people who receive fliers is multiplied by 2, not added by 5.
Pattern of distribution: This means the relationship between t and F is not linear, it's exponential because the number of people doubles each day.
Correct answer: The correct answer is (D) The relationship is exponential because F increases by a factor of 2 each time t increases by 1.
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