The population of a bacteria culture after hours is modelled by the function

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

Problem

The population

P(t)

of a bacteria culture after

t

hours is modelled by the function

P(t)=P_0\,2^{t/4}

, where

P_0

is the initial population. (i) If the culture starts with

P_0 = 5\times10^3

bacteria, form an equation to determine the time

t

when the population reaches

8\times10^4

bacteria. (ii) Solve the equation obtained in part (i) and find

t

correct to the nearest hour.