Question

The desert temperature, H, oscillates daily between 60°F at 5 am and 80°F at 5 pm. Enter a possible formula for H in terms of t, measured in hours from 5 am.

Answer 1

The formula for the desert temperature, H, in terms of t measured in hours from 5 am is H = (5/3)t + 60.

Step-by-step explanation:

The desert temperature, H, oscillates daily between 60°F at 5 am and 80°F at 5 pm. To find a possible formula for H in terms of t, measured in hours from 5 am, you can assume a linear relationship between temperature and time. We can use the equation of a straight line, y = mx + b, where y represents the temperature, x represents the time, and m and b represent constants. Let's calculate the values of m and b:

1. At 5 am, the temperature is 60°F, which corresponds to t = 0. This gives us the point (0, 60).
2. At 5 pm, the temperature is 80°F, which corresponds to t = 12. This gives us the point (12, 80).
3. Using these two points, we can find the slope (m) of the line: m = (80 - 60) / (12 - 0) = 20/12 = 5/3.
4. We can then use the point-slope form of a line to find the equation: y - 60 = (5/3)(x - 0).
5. Simplifying, we get the equation y = (5/3)x + 60.

So, a possible formula for H in terms of t is H = (5/3)t + 60.