The temperature throughout the day can be modelled by a periodic function. Below is data on temperature taken from the roof of Cypress Bay HS on November 8th, 2023. 𝑡 is given in hours after midnight and 𝑇𝑒𝑚𝑝 is given in °F
Use Desmos to plot this data and determine if it appears sinusoidal.
Assume the temperature can be modelled by a sinusoidal function
𝑓𝑡=𝑎sin𝑏𝑥+𝑐+𝑑. Use a graphing utility to find suitable values of 𝑎, 𝑏, 𝑐, and 𝑑.
What is the period of the temperature model? Does this align with what one may expect from the context of the question?
Use the model to predict what time the temperature first reached 78°F.