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Alina is an ecologist who studies the change in the bear population in Siberia over time.

The relationship between the elapsed time, [tex]t[/tex], in years, since Alina began studying the population, and the total number of bears, [tex]N(t)[/tex], is modeled by the following function:
[tex]\[ N(t) = 2187 \cdot (0.67)^t \][/tex]

Complete the following sentence about the yearly percent change of the bear population.

Every year, [tex]33\%[/tex] of bears are subtracted from the bear population in Siberia.



Answer :

GinnyAnswer
Certainly! Let's analyze the function given and articulate the yearly percent change of the bear population step by step.

The function provided is:
[tex]\[ N(t) = 2187 \cdot (0.67)^t \][/tex]

This function indicates that the bear population decreases each year, multiplied by a factor of 0.67.

To determine the yearly percent change:
1. Observe the decay factor: [tex]\( 0.67 \)[/tex]
2. The decay factor means that each year, the bear population is 67% of what it was the previous year.

To find the yearly percent change in the population:
1. Calculate the percent of the population that decreases each year. This is done by subtracting the decay factor from 1:
[tex]\[ 1 - 0.67 = 0.33 \][/tex]
2. Convert this to a percentage:
[tex]\[ 0.33 \times 100\% = 33\% \][/tex]

So, every year:
[tex]\[ 33\% \][/tex] of the bear population is subtracted.

To be precise:
Every year, 32.99999999999999% of bears are subtracted from the bear population in Siberia.

Therefore, the complete sentence is:
"Every year, 32.99999999999999% of bears are subtracted from the bear population in Siberia."

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