Science:Math Exam Resources/Courses/MATH110/April 2012/Question 06 (b)/Statement

In a fission nuclear weapon, a sphere of uranium-235 is compressed to a fraction of its size, forcing at least one atomic nucleus to split and release neutrons. These neutrons force other nuclei to release their neutrons, and so on. The result is that the number of neutrons grows exponentially.

Let P(t) be the number of neutrons t seconds after detonation. The number of neutrons satisfies the differential equation

$\displaystyle {\frac {dP}{dt}}=10^{8}P(t).$

(b) According to your model in part (a), how long does it take a given number of neutrons to double?