Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor.

Problem

A red-hot sword was plunged into cold water. This caused the temperature difference between the sword and the water to decrease rapidly.
The relationship between the elapsed time t, in seconds, since the sword was plunged into water, and the temperature difference, D, left parenthesis, t, right parenthesis, is modeled by the following function:

Complete the following sentence about the decay rate of the temperature difference.
The temperature difference is reduced by a factor of start fraction, 1, divided by, 4, end fraction every
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
seconds.