Table 1.21 gives the average monthly temperatures for St. Louis for a 12-month period starting with January.

Question:

Table 1.21 gives the average monthly temperatures for St. Louis for a 12-month period starting with January. Model the monthly temperature with an equation of the form

y in degrees Fahrenheit, t in months, as follows:

(a) Find the value of b assuming that the period is 12 months.
(b) How is the amplitude a related to the difference 80° - 30°?
(c) Use the information in (b) to find k.
(d) Find h, and write an equation for y.
(e) Superimpose a graph of y on a scatter plot of the data.