https://file.aiquickdraw.com/mathbot/file/17290135560364uzj0qa1.jpg

To find the number of black bears after 2 years, we will use the formula for exponential growth:

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

where:
- \(P_0\) is the initial population (324 bears),
- \(r\) is the annual growth rate (10%, or 0.10),
- \(t\) is the number of years (2 years).

Plugging in the values:

\[
P = 324 \times (1 + 0.10)^2
\]

\[
P = 324 \times 1.1^2
\]

\[
P = 324 \times 1.21
\]

\[
P \approx 392.04
\]

Therefore, approximately 392 black bears are expected to be in the area in 2 years.

Would you like a more detailed explanation or have any other questions? 

Here are five related questions for further exploration:
1. What would the population be after 5 years if the growth rate remained the same?
2. How would the bear population change if the growth rate was 15% per year?
3. If the bear population is expected to double in how many years will this occur?
4. What if there were initially 500 bears, how would this affect the population in 2 years?
5. How can you calculate the growth rate if you know the population after a certain number of years?

**Tip:** When calculating compound growth, it's essential to use the correct growth factor, \(1 + r\), where \(r\) is the rate expressed as a decimal.

Ana completed a study and noticed that there are 324 black bears in a certain area. She expects this population to increase by approximately 10% per year for the next several years. Approximately how many black bears will there be in 2 years?

Learn how to calculate the population of black bears after 2 years, given an initial population of 324 and an annual growth rate of 10%. This problem explores exponential growth and percentage growth, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation