Question

18. Samantha is studying the population growth of endangered birds. The growth can be modeled by the equation
B(t) =100 +35t2
, where B is the population after t, time in years.
Complete the table shown.

Answer 1

To complete the table for the population growth modeled by the equation \( B(t) = 100 + 35t^2 \), we can calculate the population for various values of \( t \) (the number of years) by substituting the values of \( t \) into the equation.

Here is a sample table format with calculations for \( t = 0, 1, 2, 3, \) and \( 4 \) years:

| Year (t) | Population B(t) = 100 + 35t² |
|----------|--------------------------------|
| 0 | \( B(0) = 100 + 35(0)^2 = 100 + 0 = 100 \) |
| 1 | \( B(1) = 100 + 35(1)^2 = 100 + 35 = 135 \) |
| 2 | \( B(2) = 100 + 35(2)^2 = 100 + 35(4) = 100 + 140 = 240 \) |
| 3 | \( B(3) = 100 + 35(3)^2 = 100 + 35(9) = 100 + 315 = 415 \) |
| 4 | \( B(4) = 100 + 35(4)^2 = 100 + 35(16) = 100 + 560 = 660 \) |

So the completed table will look like this:

| Year (t) | Population B(t) |
|----------|------------------|
| 0 | 100 |
| 1 | 135 |
| 2 | 240 |
| 3 | 415 |
| 4 | 660 |

Feel free to ask if you need further calculations for different years or additional information!