The guppy population follows an exponential growth pattern. Let's break it down:

1. Initially, a pair of guppies produces 50 offspring, with half of them (25) being females.
2. Each of these 25 females will produce 50 offspring in the next generation, giving 25 * 50 = 1,250 guppies in the second generation.
3. In the third generation, the number of guppies produced will be 25 * 1,250 = 31,250, and this process continues in the same manner.

From the given information, each generation multiplies the number of guppies by 50. Therefore, we are looking for a formula that describes exponential growth where each generation increases by a factor of 50.

Formula Derivation:

• In generation 0, there are 2 guppies (the initial pair).
• In generation 1, there are 50 guppies.
• In generation 2, there are 1,250 guppies.
• In generation 3, there are 31,250 guppies.
• And so on.

The formula for the population $y$ in terms of generation $x$ is:

$y = 50 \cdot 2^x$

This formula correctly represents the exponential growth based on the pattern in the problem.

The correct answer is: $y = 50 \cdot 2^x$

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Would you like more details on exponential growth or clarification? Here are some related questions:

1. What are some common real-life examples of exponential growth?
2. How does the population growth rate affect the overall model?
3. Can you explain why doubling time is important in exponential growth models?
4. What factors could limit the exponential growth of populations in real life?
5. How would you adjust this model if there were other factors like predation or disease?

Tip: In exponential growth models, small changes in the growth rate or generation time can lead to large differences in outcomes over time.