The population of a strain of bacteria in a nutrient solution doubles every 3 hours
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
The population of a strain of bacteria in a nutrient solution doubles every 3 hours. Initially, at time t=0, the culture contains 1.5×106 bacteria.
(i) Form an exponential function P(t) that models the population (number of bacteria) after t hours, restricting the domain to biologically meaningful values.
(ii) Using the model, calculate the population after 9 hours.
(iii) Determine the least time (to the nearest tenth of an hour) required for the population to reach 2.4×107. State whether the answer obtained lies within the chosen domain and comment briefly.