A population of wolves in a county is represented by the equation P(t) = 80(0.98)^t, where t is the number of years since 1998. Predict the number of wolves in the population in the year 2008.
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To predict the number of wolves in the population in the year 2008, we need to substitute the value of t that corresponds to the year 2008 into the equation P(t).
Step 1: Calculate the value of t for the year 2008.
Since t represents the number of years since 1998, the year 2008 is 10 years after 1998.
Therefore, t = 10.
Step 2: Substitute the value of t into the equation P(t).
P(t) = 80(0.98)^t
P(10) = 80(0.98)^10
Step 3: Calculate the population of wolves in the year 2008.
Using a calculator or mathematical software, evaluate the expression:
P(10) = 80(0.98)^10
P(10) ≈ 80(0.8179)
P(10) ≈ 65.432
Therefore, the predicted number of wolves in the population in the year 2008 is approximately 65.432.