Find the doubling time

Question

In 2003 there were 7,225 Starbucks stores. In 2005 there were 10,241 Starbucks stores. If Starbucks continues to increase exponentially at the same rate find the doubling time.

Answer 1

t = doubling time in years

2 years from 2003 to 2005 ⇒

10241 = 7225 (2)^t

Solve for t.

10241 / 7225 = 2^t

log(10241 / 7225) = t log2

t = log(10241 / 7225) / log2 = 0.5033 years