How Long Will It Take for the Moose Population on Newfoundland Island to Reach 100,000 Animals?
Understanding the dynamics of population growth, especially in ecosystems like the moose population on the island of Newfoundland, is crucial for conservation and ecological management. The population growth model given by the equation ( M 75000 (10^{5-t}) ) provides a fascinating window into how population changes over time.
Modeling Population Growth: A Step-by-Step Guide
Given the initial population of moose ( M ) on Newfoundland Island is modeled by ( M 75000 cdot 10^{5-t} ), where ( t ) represents the time in years, we can calculate the number of years it will take for the moose population to grow to 100,000 animals. This involves solving the equation:
M 75000 cdot 10^{5-t} 100000
Procedure for Problem-Solving
1. **Rewriting the equation**: We start by rearranging the given population equation to find ( t ). The equation becomes:
75000 cdot 10^{5-t} 100000
10^{5-t} frac{100000}{75000}
10^{5-t} frac{4}{3}
5 - t log_{10}left(frac{4}{3}right)
t 5 - log_{10}left(frac{4}{3}right)
2. **Calculating the logarithm**: Now, we need to find the value of ( log_{10}left(frac{4}{3}right) ). Using a calculator, or more precisely, recognizing that ( log_{10}left(frac{4}{3}right) approx 0.1249 ), we get:
t approx 5 - 0.1249
t approx 4.8751
Understanding the Result
The result indicates that it will take approximately 4.8751 years for the moose population to grow from 75,000 to 100,000 animals. This calculation is based on the exponential growth model provided in the initial equation.
Conclusion
Understanding the dynamics of population growth is essential for ecological management, especially on islands like Newfoundland. The exponential growth model ( M 75000 cdot 10^{5-t} ) helps in forecasting and planning conservation efforts. The key takeaway is that the population growth is not linear but follows an exponential curve, emphasizing the importance of addressing factors influencing population dynamics.
Related Keywords
Moose population, Newfoundland Island, exponential growth