Within two months of birth, a pair of the fish known as guppies can produce 50 offspring in the first generation. If half of those are females, each of the 25 females can produce 50 offspring. There would be 25 · 50 = 1250 guppies in the second generation, 25 · 1250 = 31,250 guppies in the third generation, and 781,250 guppies in the fourth generation. Assume this pattern continues; ignore additional births, predators, sickness, etc. Assume that 1 generation = 2 months.


------

What is the formula for the guppy population? Let y = number of guppies and x = generation.

 

Group of answer choices

y = 25 · 2x

y = 50 · 2x

y = 2 · 25x

y = 50

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:
\[
y = 50 \cdot 2^x
\]

---

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.

Within two months of birth, a pair of the fish known as guppies can produce 50 offspring in the first generation. If half of those are females, each of the 25 females can produce 50 offspring. There would be 25 · 50 = 1250 guppies in the second generation, 25 · 1250 = 31,250 guppies in the third generation, and 781,250 guppies in the fourth generation. Assume this pattern continues; ignore additional births, predators, sickness, etc. Assume that 1 generation = 2 months.

What is the formula for the guppy population? Let y = number of guppies and x = generation.

Explore the exponential growth of a guppy population over generations. Starting with 50 offspring in the first generation, learn how the population increases by a factor of 50 every two months, and find the formula y = 50 * 2^x that describes this growth. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation