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

Problem

Takumi started studying how the number of branches on his tree changes over time.
The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total number of its branches, N, left parenthesis, t, right parenthesis, is modeled by the following function:

Complete the following sentence about the yearly rate of change in the number of branches.
Every year, the number of branches
by a factor of
  • 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
.