A culture of bacteria in a laboratory satisfies the relation

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

P = 3^{t}

, where

P

(in thousands) is the population and

t

(in hours) is the time elapsed since the beginning of the experiment. (a) Express

t

explicitly as a function of

P

in logarithmic form. (b) Calculate, correct to two decimal places, the time required for the culture to reach

P = 5

. (c) For the function obtained in part (a), state its domain and range in the context of this situation and briefly justify your answer.