Question An epidemiologist is observing the growth pattern of a pathogenic bacteria. She starts with 20 bacteria that grow at a rate of \( 90 \% \) per hour. She will check on the bacteria in 16 hours. How many bacteria will she find? Round your answer to the nearest whole number. Provide your answer below: \( \square \) bacteria

To find the number of bacteria after 16 hours, we can use the formula for exponential growth, which is: \[ N = N_0 \times (1 + r)^t \] where \( N_0 \) is the initial number of bacteria, \( r \) is the growth rate, and \( t \) is the time in hours. Here, \( N_0 = 20 \), \( r = 0.90 \), and \( t = 16 \). So, \[ N = 20 \times (1 + 0.90)^{16} \] \[ N = 20 \times (1.90)^{16} \] Calculating \( (1.90)^{16} \approx 13468.2821 \), we find: \[ N \approx 20 \times 13468.2821 \approx 269365.642 \] Rounding to the nearest whole number, she will find approximately \( 269366 \) bacteria. \( 269366 \) bacteria