the chart below represents the maximum and minimum hours of sunlight recorded at two times during the year in Cosine Bay Alberta.
a) Create a function of hours of sunlight (h) vs day of the year (d)
b) use your function to find the hours of sunlight on day 90 and 250
Day of year (x) Hours of daylight (y)
182 18
350 6.5
To create a function of hours of sunlight (h) vs day of the year (d), we can use linear interpolation. Since we have two data points, we can use the equation of a line to find the relationship between the day of the year and the hours of sunlight.
Let's find the equation of the line that passes through the points (182, 18) and (350, 6.5).
First, find the slope of the line:
slope (m) = (change in y) / (change in x)
= (6.5 - 18) / (350 - 182)
= -11.5 / 168
= -0.06845
Now, we can use the point-slope form of a line to find the equation:
(y - y1) = m(x - x1)
Plugging in the values of the first point (182, 18), we get:
y - 18 = -0.06845(x - 182)
Simplifying the equation:
y - 18 = -0.06845x + 12.4659
Adding 18 to both sides:
y = -0.06845x + 30.4659
Therefore, the function of hours of sunlight (h) vs day of the year (d) is:
h = -0.06845d + 30.4659
To find the hours of sunlight on day 90 and 250, we can plug these values into the formula:
For day 90:
h = -0.06845(90) + 30.4659
h = -6.16105 + 30.4659
h ≈ 24.30485
For day 250:
h = -0.06845(250) + 30.4659
h = -17.1125 + 30.4659
h ≈ 13.3534
Therefore, on day 90, there are approximately 24.3 hours of sunlight, and on day 250, there are approximately 13.4 hours of sunlight.