Final answer:
To represent the exponential growth of bacteria every 30 minutes by 95%, the correct growth factor to use is 1.95, and the percent growth rate is 95%. This leads to the equation N(t) = 550 * 1.95^(2t), where t is in hours.
Step-by-step explanation:
The question involves an initial population of bacteria that is growing exponentially by 95% every 30 minutes. The initial count of bacteria is 550. To model this situation, we would use the formula for exponential growth:
N(t) = N_0 * e^(rt)
Where N(t) is the number of bacteria at time t, N_0 is the initial number of bacteria, r is the growth rate, and t is the time in hours. In this case, the base or growth factor is 1.95 (which represents 100% of the original plus 95% growth), and the percent growth rate within the given time interval is 95%. Therefore, the incorrect base of 0.96 must be replaced with the correct base of 1.95 to accurately represent the exponential growth.
The accurate equation to model this bacterial growth, assuming continuous growth, is:
N(t) = 550 * 1.95^(2t)
t is in hours, and since the population doubles every 30 minutes, we multiply t by 2 to convert 30 minutes into hourly intervals.