# Science:Math Exam Resources/Courses/MATH110/April 2012/Question 06 (a)

MATH110 April 2012
Other MATH110 Exams

### Question 06 (a)

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

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

(a) Write down an exponential algebraic expression for P(t) which satisfies the differential equation given above.

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