To analyze the yearly percent change in the bear population in Siberia, we begin with the given population function:
[tex]\[ N(t) = 2187 \cdot (0.67)^t \][/tex]
In this function, [tex]\( 2187 \)[/tex] represents the initial bear population, and [tex]\( 0.67 \)[/tex] is the decay factor applied each year. The decay factor tells us the proportion of the population that remains after each year.
To find the yearly percent change, we can focus on the decay factor, [tex]\( 0.67 \)[/tex], which indicates that the bear population is 67% of its value from the previous year, hence it decays.
The yearly decay percentage can be calculated as follows:
1. The decay factor is [tex]\( 0.67 \)[/tex].
2. To find out the percentage of the population that decays each year, we subtract the decay factor from 1 (which would represent 100% if there were no decay).
3. So, we compute [tex]\( 1 - 0.67 \)[/tex].
4. [tex]\( 1 - 0.67 = 0.33 \)[/tex].
5. To express this decay in percentage terms, we multiply by 100:
[tex]\[ 0.33 \times 100 = 33 \% \][/tex]
Therefore, every year, 33% of the bear population is subtracted.
Completing the sentence:
Every year, [tex]\( 33 \% \)[/tex] of bears are subtracted from the population in Siberia.
