Question 1179719
A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size.
 After 3 hours there will be 480 bacteria.
(a) Express the population P after t hours as a function of t.
{{{P(t)= p*2^(tk)}}}, where
P(t) = 480
p = 160
t = 3
k = constant
{{{160*2^(3k) = 480}}}
{{{2^(3k) = 480/160}}}
{{{2^(3k) = 3}}}
using logs
3k*ln(2) = ln(3)
3k = {{{ln(30)/ln(2)}}}
3k = 1.585
k = {{{1.585/3}}}
k = .528
The equation
{{{P(t) = p*2^(.528t)}}}
:
(b) What will be the population after 4 hours?
{{{P(t) = 160*2^(.528*4)}}}
p(t) = 692
:
(c) How long will it take for the population to reach 2770?
 Round your answer to two decimal places.
{{{160*2^(.528t) = 2770}}}
{{{2^(.528t) = 2770/160}}}
{{{2^(.528t) = 17.3125}}}
.528t = {{{ln(17.315)/ln(2)}}}
.528t = 4.1137
t = {{{4.1137/.528}}}
t = 7.79 hrs