Question
A herd of zebras is declining at a rate of 4% each year. The herd currently has 72 zebras. Of the
four functions graphed in the image, which correctly models the population decline?
The graph that correctly models the population decline is Option #
four functions graphed in the image, which correctly models the population decline?
The graph that correctly models the population decline is Option #
Answers
GPT-4o mini
To model the population decline of the herd of zebras, we can use an exponential decay function. The formula for exponential decay is:
\[ P(t) = P_0 \times (1 - r)^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the rate of decline (expressed as a decimal), and
- \( t \) is the time in years.
In this case:
- \( P_0 = 72 \) (the current population),
- \( r = 0.04 \) (4% decline).
Thus, the function modeling the population of zebras would be:
\[ P(t) = 72 \times (1 - 0.04)^t \]
\[ P(t) = 72 \times (0.96)^t \]
The correct graph to represent this function would show a continuous decline in the number of zebras over time, starting at 72 and approaching 0 as time increases.
If presented with options in the form of graphs, you should look for a graph that starts at 72 and curves downwards, showing exponential decay with a relatively gentle slope, which reflects the 4% decline each year.
Without seeing the actual graphs, I cannot identify which specific option is correct. However, look for the graph that best represents this mathematical model based on the characteristics mentioned above.
\[ P(t) = P_0 \times (1 - r)^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the rate of decline (expressed as a decimal), and
- \( t \) is the time in years.
In this case:
- \( P_0 = 72 \) (the current population),
- \( r = 0.04 \) (4% decline).
Thus, the function modeling the population of zebras would be:
\[ P(t) = 72 \times (1 - 0.04)^t \]
\[ P(t) = 72 \times (0.96)^t \]
The correct graph to represent this function would show a continuous decline in the number of zebras over time, starting at 72 and approaching 0 as time increases.
If presented with options in the form of graphs, you should look for a graph that starts at 72 and curves downwards, showing exponential decay with a relatively gentle slope, which reflects the 4% decline each year.
Without seeing the actual graphs, I cannot identify which specific option is correct. However, look for the graph that best represents this mathematical model based on the characteristics mentioned above.