From the given table, we have:
Day (t) C(t)
2 314
4 356
6 370
8 386
10 405
12 442
14 516
Let's estimate the value of C'(8).
To find the value of C'(8), let's first find the upper and lower values.
Using the formula:
[tex]\frac{C(B)-C(A)}{B-A}[/tex]We have:
[tex]\begin{gathered} C^{\prime}(8)_{upper}=\frac{C(10)-C(8)}{10-8}=\frac{405-386}{2}=\frac{19}{2}=9.5 \\ \\ C^{\prime}(8)_{lower}=\frac{C(8)-C(6)}{8-6}=\frac{386-370}{2}=\frac{16}{2}=8 \end{gathered}[/tex]Therefore, the value of C'(8) will be:
[tex]C^{\prime}(8)=\frac{C^{\prime}(8)_{uper}+C^{\prime}(8)_{lower}}{2}=\frac{9.5+8}{2}=\frac{17.5}{2}=8.75[/tex]Therefore, the value of C'(8) is 8.75 calories per day.
• ANSWER:
B. 8.75 calories per day.
