An investor is presented with a choice of two investments: an established clothing store and a new computer store. Each choice requires the same initial investment and each produces a continuous income stream of $4\%,$ compounded continuously. The rate of flow of income from the clothing store is $f(t)=12,000,$ and the rate of flow of income from the computer store is expected to be $g(t)=10,000e^{0\mathrm{.}05t}.$ Compare the future values of these investments to determine which is the better choice over the next $5$ years.