Let's solve the population model given by the equation \( B(t) = 100 + \frac{3}{5}t^2 \) for \( t = 2 \) and \( t = 5 \).
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Calculate \( B(2) \): \[ B(2) = 100 + \frac{3}{5}(2^2) \] \[ B(2) = 100 + \frac{3}{5}(4) \] \[ B(2) = 100 + \frac{12}{5} \] \[ B(2) = 100 + 2.4 = 102.4 \]
So, the interpretation is:
- After 2 years, the population is approximately 102 birds.
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Calculate \( B(5) \): \[ B(5) = 100 + \frac{3}{5}(5^2) \] \[ B(5) = 100 + \frac{3}{5}(25) \] \[ B(5) = 100 + \frac{75}{5} \] \[ B(5) = 100 + 15 = 115 \]
So the interpretation is:
- After 5 years, the population is 115 birds.
Based on the calculations:
1: After 2 years, the population is approximately 102 birds.
2: After 5 years, the population is 115 birds.
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