To determine whether the graph accurately models the situation given, we need to consider the exponential growth of the rabbits. The initial population of rabbits is 25, and with a growth rate of 50% per month, the population can be modeled by the exponential growth formula:
\[ P(t) = P_0 \cdot (1 + r)^t \]
where:
- \( P_0 \) is the initial population (25 rabbits),
- \( r \) is the growth rate (0.5 for 50%),
- \( t \) is the time in months.
This means after one month, the population will be:
\[ P(1) = 25 \cdot (1 + 0.5)^1 = 25 \cdot 1.5 = 37.5 \]
After two months:
\[ P(2) = 25 \cdot (1.5)^2 = 25 \cdot 2.25 = 56.25 \]
And so forth. This represents an exponential growth pattern.
Now, without having the actual visual of the graph, if the L-shaped curve does not represent this kind of exponential growth, it would not be an accurate model of the rabbits' population increase.
So, if the graph shows steady increases (linear growth) instead of a steep upward curve (exponential growth), it would not accurately represent the situation.
Since I cannot see the actual graph, my final answer would be based on the typical understanding of exponential growth versus what you might observe in an L-shaped curve.
Thus, I would answer with 2 for no, assuming the graph does not show exponential growth.
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