A biologist studying a population of geckos for several years found that the population can be modeled as shown below, where P** is the population, and t** is the time in years.

P=230⁢(1.04)t

What is the growth rate of this population?

Responses

4%

4 %

6%

6 %


The population growth model provided is:

\[
P = 230(1.04)^t
\]

This model is in the form of exponential growth, which can be written as:

\[
P = P_0 (1 + r)^t
\]

Where:
- \( P_0 \) is the initial population,
- \( r \) is the growth rate,
- \( t \) is the time in years.

Here, \( 1 + r = 1.04 \), meaning that the growth rate \( r \) is 0.04 or **4%**.

So, the growth rate of this population is **4%**.

Would you like a detailed explanation of exponential growth, or do you have any other questions?

Here are some related questions:
1. How do you calculate the population at any given year using this model?
2. What happens to the population if the growth rate increases to 6%?
3. How can we determine the doubling time for this population?
4. What is the significance of exponential growth in biological populations?
5. How would you modify the equation if the population decreases by 4% annually?

**Tip:** In exponential growth models, the base of the exponential term (1 + r) directly represents the growth factor.

A biologist studying a population of geckos for several years found that the population can be modeled as shown below, where P is the population, and t is the time in years. P = 230(1.04)^t. What is the growth rate of this population?

Explore how to calculate the growth rate of a gecko population using the exponential growth model P = 230(1.04)^t. Learn key algebraic concepts related to exponential functions, and find out how a 4% annual growth rate is derived from the model. Ideal for Grades 9-12 biology and algebra students.

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