A culture of bacteria grows according to the law

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

N(t)=N_{0}e^{kt}

, where

N(t)

is the number of bacteria present after

t

hours,

N_{0}

is the initial number, and

k

is a positive constant. (i) Show that the time

T

required for the population to double satisfies

T=\dfrac{\ln 2}{k}

. (ii) The culture initially contains

500

bacteria. After

3

hours the count is

800

. Determine the value of

k

correct to four decimal places. (iii) Using the value of

k

found in part (ii), calculate the time (to the nearest minute) at which the population will reach

2000