https://file.aiquickdraw.com/mathbot/file/1726904303674330hsx4s.jpg

The question asks which of the statements is best modeled by exponential growth. Let's analyze the options:

- **A. The population grows 5% every year.**  
  This describes exponential growth because the population increases by a fixed percentage each year. Exponential growth occurs when something grows by a constant percentage over time. The formula would be \( P(t) = P_0 (1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (5% or 0.05 in this case), and \( t \) is time.

- **B. The cost of an apple per kilogram.**  
  The cost of an apple doesn't necessarily follow exponential growth. Prices can fluctuate or increase, but they are not inherently modeled by exponential growth without more context.

- **C. The area of a square of the side \( s \).**  
  The area of a square is modeled by \( A = s^2 \), which is quadratic growth, not exponential.

- **D. The height of a person with respect to his age.**  
  Human height grows linearly during childhood and adolescence and then stabilizes, so this is not exponential growth.

### Answer: **A. The population grows 5% every year** is the correct choice.

Would you like more details on exponential growth or have any questions?

Here are 5 related questions to deepen your understanding:
1. What are the key differences between linear, quadratic, and exponential growth?
2. How would you model decay processes using exponential functions?
3. Can exponential growth continue indefinitely in real-world scenarios?
4. What is the formula for compound interest, and how does it relate to exponential growth?
5. How would doubling time relate to exponential growth?

**Tip:** Exponential growth is characterized by a constant percentage increase, while linear growth adds a fixed amount each time.

Which of the statements is best modeled by an exponential growth?
A. The population grows 5% every year.
B. The cost of an apple per kilogram.
C. The area of a square of the side s.
D. The height of a person with respect to his age.

Understand which of the given scenarios best represents exponential growth. Explore how a population growing at 5% annually follows an exponential model. This problem is ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation