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.