A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was $64$ . The number increased by $50$ percent each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by $50$ percent per year. What is the difference in the number of chickens between these two situations two years from now? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $\mathbf{1 8 9}$ $\newline$ (C) $405$ $\newline$ (D) $11$

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Q. A poultry farmer has been keeping track of the number of chickens at his farm over previous years. Four years ago, the number of chickens was

64

. The number increased by

50

percent each year for four years until the present day. In the future, the farmer considers the situation where the number of chickens increases at a constant rate equal to the rate of the most recent year or the situation where the number continues to increase by

50

percent per year. What is the difference in the number of chickens between these two situations two years from now?

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

\mathbf{1 8 9}

\newline

(C)

405

\newline

(D)

11

Calculate Present Day Chickens: First, calculate the number of chickens at the present day after increasing by $50$ percent each year for four years starting from $64$ chickens. $\newline$ Year $1$ : $64 \times 1.5 = 96$ chickens $\newline$ Year $2$ : $96 \times 1.5 = 144$ chickens $\newline$ Year $3$ : $144 \times 1.5 = 216$ chickens $\newline$ Year $4$ (Present Day): $216 \times 1.5 = 324$ chickens
Calculate Chickens Two Years Later (Scenario $1$ ): Next, calculate the number of chickens two years from now if the number continues to increase by $50$ percent per year. $\newline$ Year $1$ (Future): $324 \times 1.5 = 486$ chickens $\newline$ Year $2$ (Future): $486 \times 1.5 = 729$ chickens
Calculate Chickens Two Years Later (Scenario $2$ ): Now, calculate the number of chickens two years from now if the number increases at a constant rate equal to the rate of the most recent year. The most recent increase was from $216$ to $324$ chickens, which is an increase of $324 - 216 = 108$ chickens per year. $\newline$ Year $1$ (Future): $324 + 108 = 432$ chickens $\newline$ Year $2$ (Future): $432 + 108 = 540$ chickens
Find Difference in Chickens: Finally, find the difference in the number of chickens between the two future scenarios two years from now. $\newline$ Difference: $729$ (Scenario $1$ ) - $540$ (Scenario $2$ ) = $189$ chickens