We appreciate your visit to Dr Howard is studying an endangered fox whose population is declining by 7 5 every year If there are currently 2 913 foxes how many. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
Using the formula for exponential decay, approximately 1,498 foxes will remain in 7 years.
Explanation:
To find out how many foxes will remain in 7 years, we need to use exponential decay. The formula for exponential decay is A = P(1 - r)^t, where A is the final amount, P is the initial amount, r is the decay rate per time period (as a decimal), and t is the number of time periods. In this case, the initial amount of foxes is 2,913 and the decay rate is 7.5% or 0.075. We can plug in these values to the formula and calculate the final amount:
A = 2,913(1 - 0.075)^7
Simplifying the equation:
A ≈ 2,913(0.925)^7
A ≈ 2,913(0.514)
A ≈ 1,497.66
Therefore, approximately 1,498 foxes will remain in 7 years.
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Final Answer:
In 7 years, there will be approximately 1,379 foxes remaining due to a 7.5% annual decline from the current population of 2,913 foxes. This decline reflects the ongoing threat to the endangered fox population.
Explanation:
To calculate the future fox population, we can use the formula for exponential decay:
[tex]N(t) =[/tex][tex]N_0[/tex] *[tex](1 - r)^t[/tex]
Where:
- N(t) is the future population.
- [tex]\(N_0\)[/tex] is the current population (2,913 foxes).
- r is the annual decline rate (7.5% or 0.075 as a decimal).
- t is the number of years (7 years in this case).
Plugging in these values:
N(7) = 2,913 * (1 - 0.075)⁷
Calculating this:
N(7) ≈ 1,379
So, in 7 years, there will be approximately 1,379 foxes remaining in the population.
This calculation shows the impact of a 7.5% annual decline on the fox population over time. It's essential to monitor and address such declines to protect endangered species like these foxes.
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