Question

“clutch size” is the number of eggs that a female bird lays in one nest attempt. the table below shows how average clutch size for eastern bluebirds, $c$, varied with the date on which the last egg in a clutch was laid, where $d$ is the number of days since january 1st.

$d$	60	78	96	114	132	150	166	180
$c(d)$	4.5	4.4	4.7	4.7	4.6	4.5	4.2	3.6

a. find $c(132)$ and select its units.
$c(132)=$ 4.6 eggs
b. solve $c(d)=3.6$ and select the units of your answer.
$d =$ 180 days
c. calculate net change in $c$ from $d = 132$ to $d = 166$ and select its units. if needed, round your answer to 4 decimal places.
-0.4 eggs
d. calculate average rate of change in $c$ from $d = 132$ to $d = 166$ and select its units. if needed, round your answer to 4 decimal places.

Explanation:

Step1: Find $C(132)$

Look at the table. When $d = 132$, $C(132)=4.6$ and the unit of $C$ is eggs.

Step2: Solve $C(d)=3.6$

Look at the table. When $C(d) = 3.6$, $d = 180$ and the unit of $d$ is days.

Step3: Calculate net - change in $C$ from $d = 132$ to $d = 166$

The net - change formula is $\Delta C=C(166)-C(132)$. From the table, $C(166) = 4.2$ and $C(132)=4.6$. So $\Delta C=4.2 - 4.6=- 0.4$ eggs.

Step4: Calculate average rate of change in $C$ from $d = 132$ to $d = 166$

The average rate of change formula is $\frac{\Delta C}{\Delta d}=\frac{C(166)-C(132)}{166 - 132}$. We know $C(166) = 4.2$, $C(132)=4.6$, and $\Delta d=166 - 132 = 34$. So $\frac{4.2-4.6}{34}=\frac{-0.4}{34}\approx - 0.0118$ eggs per day.

Answer:

a. $C(132)=4.6$, units: eggs
b. $d = 180$, units: days
c. Net - change: $-0.4$, units: eggs
d. Average rate of change: $-0.0118$, units: eggs per day