Question
Ana completed a study and noticed that there are 324 black bears in a certain area. She expects this population to increase by approximately 10% per year for the next several years.
Which equation represents the approximate number of black bears (b) in y years?
A. b=324+0.1y
B. b=324(0.1)y
C. b=324+(1.1)^y
D. b=324(1.1)^y
Fill in the Blank Question
Approximately how many black bears will there be in 2 years?
______ black bears
Which equation represents the approximate number of black bears (b) in y years?
A. b=324+0.1y
B. b=324(0.1)y
C. b=324+(1.1)^y
D. b=324(1.1)^y
Fill in the Blank Question
Approximately how many black bears will there be in 2 years?
______ black bears
Answers
GPT-4o mini
To model the population of black bears that increases by approximately 10% per year, you can use the exponential growth formula. The correct equation from the options provided is:
**D. \( b = 324(1.1)^y \)**
This equation indicates that the initial population of bears is 324, and each year the population increases by a factor of 1.1 (which is a 10% increase).
Now, to find out how many black bears there will be in 2 years, we can substitute \( y = 2 \) into the equation:
\[
b = 324(1.1)^2
\]
Calculating \( (1.1)^2 \):
\[
(1.1)^2 = 1.21
\]
Now substituting back into the equation:
\[
b = 324 \times 1.21 \approx 392.04
\]
Since the number of bears must be a whole number, we round this to the nearest whole number, which gives us approximately:
**392 black bears**
So, in 2 years, there will be approximately **392 black bears**.
**D. \( b = 324(1.1)^y \)**
This equation indicates that the initial population of bears is 324, and each year the population increases by a factor of 1.1 (which is a 10% increase).
Now, to find out how many black bears there will be in 2 years, we can substitute \( y = 2 \) into the equation:
\[
b = 324(1.1)^2
\]
Calculating \( (1.1)^2 \):
\[
(1.1)^2 = 1.21
\]
Now substituting back into the equation:
\[
b = 324 \times 1.21 \approx 392.04
\]
Since the number of bears must be a whole number, we round this to the nearest whole number, which gives us approximately:
**392 black bears**
So, in 2 years, there will be approximately **392 black bears**.