Step 1 :The problem is a differential equation problem. The rate of growth of the bacteria is given by \(20e^{t/4}\). We also know the initial condition, that at t=0, the number of bacteria is 23000. We need to find the number of bacteria at t=4.
Step 2 :To solve this, we can integrate the rate of growth function from 0 to 4, and add the initial number of bacteria.
Step 3 :\[\int_{0}^{4} 20e^{t/4} dt + 23000\]
Step 4 :Calculate the integral to get the number of bacteria at t=4.
Step 5 :\[\boxed{23137}\]