mRNA transcription The intermediate molecule mRNA arises in the decoding of DNA: it is produced by a process called transcription and it eventually decays. Suppose that the rate of transcription is changing exponentially according to the expression ebt, where b is a positive constant and mRNA has a constant per capita decay rate of k. The number of mRNA transcript molecules T thus changes as dT dt

− ebt 2 kT Although the form of this equation is similar to that from Exercise 43, the first term on the right side is now timevarying.

As a result, the differential equation is no longer separable; however, the equation can be solved using the change of variables ystd − ekt Tstd. Solve the differential equation using this technique.