Question

Thaddeus models the number of hours of daylight in his townas

Answer 1

We have the following function

$D(t)=2.5\sin\frac{\pi t}{6}+12$

The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.

Then let's find the maximum, that happens when the sin value is 1

$\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}$

And the minimum, when sin value is -1

$\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}$

Then the least: 9.5 hours; greatest: 14.5 hours.