Question

The number of bees in a certain county is changing according to the function
f
(
t
)
=
300
(
0.94
)
t
, where t = time in years and f(t) = bee population in millions. Which statement describes this situation?

A.
The bee population is decreasing by 6% per year.

B.
The bee population is decreasing by 94% per year.

C.
The bee population is increasing by 6% per year.

D.
The bee population is increasing by 94% per year.

Answer 1

The given function for the bee population is \( f(t) = 300(0.94)^t \), where \( t \) is the time in years and \( f(t) \) represents the population in millions.

To understand how the population is changing, let's analyze the factor \( 0.94 \).

- The coefficient \( 300 \) represents the initial population when \( t = 0 \).
- The factor \( (0.94)^t \) indicates how the population changes over time.

Since \( 0.94 < 1 \), this implies that the population is decreasing over time. Specifically, the percentage decrease can be calculated as:

\[
1 - 0.94 = 0.06 \quad \text{or} \quad 6\%
\]

Therefore, the bee population is decreasing by \( 6\% \) per year.

The correct statement is:

**A. The bee population is decreasing by 6% per year.**