Question

two birds build a nest. bird a flies toward the nest at the same time bird b flies away from it. the equation $d = -12t + 96$ gives bird a’s distance from the nest in meters, $d$, as a function of time in seconds, $t$. the graph shows bird b’s distance from the nest over time.
determine whether each statement about the birds is true.
select true or false for each statement.

1. bird b is flying slower than bird a.
2. the difference in the distance between the birds at $t = 0$ is 96 m.
3. the difference between the speeds of the birds is 20 m per second.
4. bird a, the bird that is flying toward the nest, is farther from the nest than bird b when $t > 4.8$.

Explanation:

Step1: Find Bird A's speed

For Bird A, distance function is $d = -12t + 96$. The coefficient of $t$ is speed magnitude: $12$ m/s.

Step2: Find Bird B's speed

From Bird B's graph: at $t=4$, $d=24$. Speed $=\frac{24}{4}=8$ m/s.

Step3: Evaluate Statement 1

Bird B's speed (8 m/s) < Bird A's (12 m/s). So statement is True.

Step4: Evaluate Statement 2

At $t=0$: Bird A: $d=-12(0)+96=96$ m; Bird B: $d=0$ m. Difference: $96-0=96$ m. Statement is True.

Step5: Evaluate Statement 3

Speed difference: $12-8=4$ m/s, not 20. Statement is False.

Step6: Evaluate Statement 4

Set distances equal: $-12t+96=8t$. Solve: $96=20t$, $t=4.8$. For $t>4.8$, Bird A's distance: $d=-12t+96$ (decreasing), Bird B's: $d=8t$ (increasing). So Bird A is closer. Statement is False.

Answer:

1. Bird B is flying slower than Bird A.: True
2. The difference in the distance between the birds at $t = 0$ is 96 m.: True
3. The difference between the speeds of the birds is 20 m per second.: False
4. Bird A, the bird that is flying toward the nest, is farther from the nest than Bird B when $t > 4.8$.: False