The population of deer in Yosemite Valley has an annual growth rate of
11
%
11%​ per year. If there were a total of
17
,
200
17,200​ deer in the year
2018
2018​, how many will there be predicted in the year
2026
2026​? Round your answer to the nearest whole number.

To determine the population of deer in Yosemite Valley in 2026, given an annual growth rate of 11%, we can use the formula for exponential growth:

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

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the number of years.

Given:
- \( P_0 = 17,200 \) (initial population in 2018),
- \( r = 0.11 \) (11% growth rate),
- \( t = 2026 - 2018 = 8 \) years.

Plugging in these values, we get:

\[ P(8) = 17,200 \times (1 + 0.11)^8 \]

First, calculate \( (1 + 0.11)^8 \):

\[ (1.11)^8 \approx 2.3135 \]

Next, multiply this by the initial population:

\[ P(8) \approx 17,200 \times 2.3135 \approx 39,791.1 \]

Rounding to the nearest whole number:

\[ P(8) \approx 39,791 \]

Therefore, the predicted population of deer in Yosemite Valley in the year 2026 is approximately **39,791**.

Would you like any further details or have any questions?

Here are 8 related questions:
1. What would the population be in 2030 if the growth rate remains the same?
2. How does changing the growth rate to 9% affect the population in 2026?
3. What would the population be if the initial population was 20,000 instead of 17,200?
4. How many years would it take for the population to double at the current growth rate?
5. If a sudden event reduces the population by 5% in 2024, what would be the new population in 2026?
6. What is the formula for calculating the continuous growth of a population?
7. How would a decrease in the annual growth rate to 5% impact the population in 2026?
8. What other factors could influence the deer population growth besides the annual growth rate?

**Tip:** When working with exponential growth, always ensure to convert percentage rates to decimals by dividing by 100 before using them in calculations.

Explore how to predict the deer population growth in Yosemite Valley by 2026 using the exponential growth formula. Given an initial population of 17,200 in 2018 and an annual growth rate of 11%, learn how to calculate the predicted population. Discover related questions about future population estimates and the impact of changing growth rates.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation