In a certain geographic location, a herd of antelopes is declining at a rate of six percent every year. If there are currently 570 antelopes in the herd, create an exponential decay function to model the problem. If the decrease in population continues at this rate, how many antelopes will be in the herd after 10 years? Round your answer to the nearest whole number.(1 point)After 10 years there will beantelopes.
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The exponential decay function can be represented as: P(t) = P0 * (1 - r)^t, where P(t) is the population at time t, P0 is the initial population, r is the decay rate and t is the time in years.
Given that the rate of decline is six percent (or 0.06) and the current population is 570, the exponential decay function becomes:
P(t) = 570 * (1 - 0.06)^t
To find the population after 10 years, substitute t = 10 into the equation:
P(10) = 570 * (0.94)^10
P(10) ≈ 570 * 0.55839496297
P(10) ≈ 318.5281047489
Rounding to the nearest whole number, there will be approximately 319 antelopes in the herd after 10 years.
I apologize for the mistake. Let me recalculate the answer correctly.
The exponential decay function for the problem can be represented as: P(t) = P0 * (1 - r)^t, where P(t) is the population at time t, P0 is the initial population, r is the decay rate, and t is the time in years.
Given that the rate of decline is six percent (or 0.06) and the current population is 570, the exponential decay function becomes:
P(t) = 570 * (1 - 0.06)^t
To find the population after 10 years, substitute t = 10 into the equation:
P(10) = 570 * (0.94)^10
P(10) ≈ 570 * 0.563002016
P(10) ≈ 320.431130248
Rounding to the nearest whole number, there will be approximately 320 antelopes in the herd after 10 years.