A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256 \( \mathrm{~mm}^{2} \), and the bacterial

To solve this problem, we need to find the initial number of bacteria in the petri dish and the rate at which they grow. Let's denote: - \( N_0 \) as the initial number of bacteria in the petri dish. - \( r \) as the rate of growth of the bacteria. The area of the petri dish is given as 256 \( \mathrm{~mm}^{2} \). Since the bacteria grow at an exponential rate, the number of bacteria at any time \( t \) can be represented by the formula: \[ N(t) = N_0 \times e^{rt} \] Given that the area of the petri dish is 256 \( \mathrm{~mm}^{2} \), we can relate the number of bacteria to the area of the petri dish. However, we need more information about the initial number of bacteria and the rate of growth to solve for \( N_0 \) and \( r \). Please provide the initial number of bacteria and the rate of growth to proceed with the solution.