The number of bacteria in a culture, $N(t)$, after $t$ hours, is modeled by an exponential function. At $t=3$ hours, there were 1600 bacteria. At $t=5$ hours, there were 6400 bacteria. Which of the following equations represents the number of bacteria at time $t$, such that the initial number of bacteria (at $t=0$) is explicitly shown as the coefficient?