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hsan is having a big going-out-of-business sale and he wants to advertise is sale. He starts by making a large number of advertising fliers for his sale nd gives 5 of his friends many fliers. He asks each of them to give fliers to of their friends the next day, and to tell each of their friends to give fliers o 2 of their friends the day after, and so on. Let
F be the number of eople who will be given fliers on day
t. Which of the following best xplains the relationship between
t and
F ?

hsan is having a big going-out-of-business sale and he wants to advertise is sale. He starts by making a large number of advertising fliers for his sale nd gives $5$ of his friends many fliers. He asks each of them to give fliers to of their friends the next day, and to tell each of their friends to give fliers o $2$ of their friends the day after, and so on. Let $F$ be the number of eople who will be given fliers on day $t$ . Which of the following best xplains the relationship between $t$ and $F$ ?

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Solve word problems by finding two-variable equations

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Q. hsan is having a big going-out-of-business sale and he wants to advertise is sale. He starts by making a large number of advertising fliers for his sale nd gives

5

of his friends many fliers. He asks each of them to give fliers to of their friends the next day, and to tell each of their friends to give fliers o

2

of their friends the day after, and so on. Let

F

be the number of eople who will be given fliers on day

t

. Which of the following best xplains the relationship between

t

and

F

?

Understand Distribution Pattern: Understand the pattern of distribution of fliers. $\newline$ Hassan gives $5$ of his friends fliers on the first day. Each of these friends gives fliers to $2$ of their friends the next day, and those friends give fliers to $2$ more friends the following day, and so on.
Establish $t$ and $F$ Relationship: Establish the relationship between $t$ and $F$ . On the first day ( $t = 1$ ), $F = 5$ because Hassan gives fliers to $5$ friends. On the second day ( $t = 2$ ), each of these $5$ friends gives fliers to $2$ friends, so $F$ $0$ . On the third day ( $F$ $1$ ), each of the friends from the second day gives fliers to $2$ more friends, so $F$ $3$ , and so on.
Generalize into Formula: Generalize the pattern into a formula. $\newline$ The number of people who receive fliers on day $t$ is equal to $5$ times $2$ raised to the power of $(t - 1)$ , because the pattern starts with $5$ and doubles each day. $\newline$ $F = 5 \times 2^{(t - 1)}$
Verify with Given Pattern: Verify the formula with the given pattern. $\newline$ For $t = 1$ , $F = 5 \times 2^{(1 - 1)} = 5 \times 2^0 = 5 \times 1 = 5$ , which matches the initial condition. $\newline$ For $t = 2$ , $F = 5 \times 2^{(2 - 1)} = 5 \times 2^1 = 5 \times 2 = 10$ , which matches the pattern of each friend giving fliers to $2$ friends. $\newline$ For $t = 3$ , $F = 5 \times 2^{(3 - 1)} = 5 \times 2^2 = 5 \times 4 = 20$ , which also matches the pattern of the distribution doubling each day.

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