The function T(n) = 2^n describes the number of steps taken in microseconds. 5 billion years is 5e9·365·24·3600·1e6 = 1.5768e23 microseconds. need to find largest integer n such that T(n) ≤ 1.5768e23. T(n) ≤ 1.5768e23 ⇒ 2^n ≤ 1.5768e23 ⇒ log₂ 2^n ≤ log₂ 1.5768e23 ⇒ n ≤ log₂ 1.5768e23 ⇒ n ≤ 77.061... ⇒ n = 77