In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of \( 2.5 \% \) per hour. Find the bacteria at the end of 2 hours if the count was initially \( 5,06,000 \)

To find the bacterial count after 2 hours, we use the formula for exponential growth: \[ N(t) = N_0 \times (1 + r)^t \] where: - \( N_0 = 5,06,000 \) (initial count), - \( r = 2.5\% = 0.025 \) (growth rate), - \( t = 2 \) hours. Plugging in the values: \[ N(2) = 5,06,000 \times (1 + 0.025)^2 \] Calculating the growth factor for 2 hours: \[ (1 + 0.025)^2 = 1.025^2 \approx 1.050625 \] Now, calculating: \[ N(2) \approx 5,06,000 \times 1.050625 \approx 5,32,031 \] So, after 2 hours, the bacteria count will be approximately \( 5,32,031 \).