To determine the correct equation for the decline of honeybee populations over time, we can start by analyzing the decline rate and how it affects the population.
Given that the honeybee population is declining at a rate of 30% per year, it means that 70% of the population remains each year. Therefore, the population after \(n\) years can be expressed as:
\[ \text{Population after } n \text{ years} = \text{Initial population} \times (1 - \text{decline rate})^n \]
In this case:
- Initial population = 500,000
- Decline rate = 0.30
- After 1 year, the remaining population will be \( 500,000 \times 0.70 \).
Thus, the equation for the population remaining after \(n\) years will be:
\[ 500000 \times (0.70)^n \]
We want to find out when this population equals 100,000:
\[ 500000 \times (0.70)^n = 100000 \]
Looking at the answer options provided, the correct equation is:
B. \( 500000 \times (0.70)^n = 100000 \)