In 2006, it was estimated that honeybee populations were declining at a rate of 30% per year. At that time, there were approximately 500,000 honeybees.

Question

Which equation can be used to find the number of years, n, it will take for the population to be 100,000?

Answer options with 4 options
A.
500000 left-parenthesis 0.30 right-parenthesis Superscript n Baseline equals 100000

B.
500000 left-parenthesis 0.70 right-parenthesis Superscript n Baseline equals 100000

C.
500000 left-parenthesis 0.30 n right-parenthesis equals 100000

D.
500000 left-parenthesis 0.70 n right-parenthesis equals 100000

Answer 1

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. \( 500000 \times (0.70)^n = 100000 \)