Question

The number of hours of daylight y for day x (x = 1 to 365) in Anchorage, Alaska, can be modeled by y=7.0sin(2π365x−1.4)+12.4. What is the minimum number of hours of daylight in Anchorage?

Answer 1

5.4 hours

Explanation:

As the number of hours of daylight y is modeled as a function of sin, and sin has the minimum value of -1. Therefore

`sin(2\pi 365x-1.4) \geq -1`

`7sin(2\pi 365x-1.4) \geq -7`

`7.0sin(2\pi 365x-1.4)+12.4 \geq 5.4`

`y \geq 5.4`

So the minimum number of hours of daylight in Anchorage is 5.4 hours