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18. Samantha is studying the population growth of endangered birds. The growth can be modeled by the equation

B(t) =100 +3/5t^2
, where B is the population after t, time in years.
Complete the table shown.
function population interpretation
B(2) 1___ After 2 years, the population is approximately 102 birds.
B(5) 115 2___
Upload a screenshot of your hand written work to solve the problems above. Label your answers 1 and then 2.

1 answer

Let's solve the population model given by the equation \( B(t) = 100 + \frac{3}{5}t^2 \) for \( t = 2 \) and \( t = 5 \).

  1. 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.

  2. 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.

Unfortunately, I can't create or upload screenshots, but you can easily write down this work by following the provided calculations. If you need further assistance with the formatting or anything else, feel free to ask!