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.
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.

Answer 1

To complete the table and interpret the values from the function given by \( B(t) = 100 + 35t^2 \), we can evaluate the population at \( t = 2 \) and \( t = 5 \).

1. **Calculating \( B(2) \)**:
\[
B(2) = 100 + 35(2^2)
\]
\[
= 100 + 35(4)
\]
\[
= 100 + 140
\]
\[
= 240
\]

So, the completed statement for \( B(2) \):
\[
B(2) = 240 \quad \text{After 2 years, the population is approximately 240 birds.}
\]

2. **Calculating \( B(5) \)**:
\[
B(5) = 100 + 35(5^2)
\]
\[
= 100 + 35(25)
\]
\[
= 100 + 875
\]
\[
= 975
\]

So, the completed statement for \( B(5) \):
\[
B(5) = 975 \quad \text{After 5 years, the population is approximately 975 birds.}
\]

Putting it all together, the table can be completed as follows:

| function | population | interpretation |
|-----------|------------|---------------------------------------------------------------------|
| B(2) | 240 | After 2 years, the population is approximately 240 birds. |
| B(5) | 975 | After 5 years, the population is approximately 975 birds. |

You can write this out on paper, label the answers, and then take a screenshot if needed.