Consider the following equation A Pert a Solve for t t Sol

Consider the following equation. A = Pe^rt (a) Solve for t. t =

Solution

(a).We have A = Pe^rt so that P = A/e^rt.

(b). We have A = Pe^rt. On taking natural log of both the sides, we get ln A = ln Pe^rt = ln P +ln e^rt = ln P+ rt ln e = ln P + rt or, rt = (ln A-ln P). Hence t =(ln A-ln P)/r. ( as logab = log a +log b, log a^b = b log a and ln e = 1).