A hot brick is removed from a kiln and set on the floor to cool. Let t be time in minutes after…
A hot brick is removed from a kiln and set on the floor to cool. Let t be time in minutes after the brick was removed. The difference, D(t), between the brick’s temperature, initially 350◦F, and room temperature, 70◦F, decays exponentially over time at a rate of 3% per minute. The brick’s temperature, H(t), is a transformation of D(t). Find a formula for H(t). Compare the graphs of D(t) and H(t), paying attention to the asymptotes.
Let T(d) give the average temperature in your hometown on the dthday of last year (so d = 1 is January 1, etc).
(a) Graph T (d) for 1 ≤ d ≤ 365.
(b) Give a possible value for each of the following: T(6); T(100); T(215); T(371).
(c) What is the relationship between T(d) and T(d + 365)? Explain.
(d) If you graph w(d) = T (d + 365) on the same axes as T (d), how would the two graphs compare?
(e) Do you think the function T (d) + 365 has any practical significance? Explain.