To find the solution to this problem, we need to use the formula for exponential decay. The formula is:N(t) = N0 * e^(-kt)Where N(t) is the amount after a given time t, N0 is the initial amount, e is the base of the natural logarithm (approximately 2.71828), k is the decay constant, and t is the time.To find the decay constant k, we can use the given values. Let's assign the variables as follows:N(t) = 3000N0 = 8000t = 10We can substitute these values into the formula:3000 = 8000 * e^(-k * 10)Next, we can isolate e^(-k * 10) by dividing 8000 on both sides:3000/8000 = e^(-k * 10)0.375 = e^(-k * 10)To solve for k, we can take the natural logarithm of both sides of the equation:ln(0.375) = ln(e^(-k * 10))Using the property of logarithms, ln(e^x) = x:ln(0.375) = -k * 10Solving for k:k = -ln(0.375)/10Using a calculator, we find that:k ≈ 0.1604Therefore, the formula for the decay is:N(t) = 8000 * e^(-0.1604t)Now, to find the value after 25 years (t = 25), we can substitute this value into the formula:N(25) = 8000 * e^(-0.1604 * 25)Using a calculator, we find that:N(25) ≈ 3156So, the population is expected to be approximately 3156 after 25 years.
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