Question

Thaddeus models the number of hours of daylight in his town asD(t) = 3sin(pi/6•t) + 12, where D is the number of daylight hours and t is thetime in months since January 1.What are the least and greatest numbers of daylight hours over the course ofa year?

Answer 1

Step 1

Find the height value of the amplitude

`\text{The highest value of the amplitude is 3}`

Step 2

Find the greatest number of daylight hours over the course of the year, D

`D=\text{ 3 +12 = 15 hrs}`

Step 3

Find the least value of the amplitude

`\begin{gathered} \text{The least value of the amplitude = -3} \\ \end{gathered}`

Step 4

Find the least number of daylight hours over the course of the year, D

`D=\text{ -3+12=9 hours}`

Hence, the greatest number of daylight hours over the course of the year = 15 hours

and

the least number of daylight hours over the course of the year = 9 hours

Hence option C is correct.