The population P t of a culture of bacteria grows exponentially for the first 72 hr according to the model P t = P 0 e k t . The variable t is the time in hours since the culture is started. The population of bacteria is 60 , 000 after 7 hr . The population grows to 80 , 000 after 12 hr . a. Determine the constant k to 3 decimal places. b. Determine the original population P 0 . Round to the nearest thousand. c. Determine the time required for the population to reach 300 , 000 . Round to the nearest hour.
The population P t of a culture of bacteria grows exponentially for the first 72 hr according to the model P t = P 0 e k t . The variable t is the time in hours since the culture is started. The population of bacteria is 60 , 000 after 7 hr . The population grows to 80 , 000 after 12 hr . a. Determine the constant k to 3 decimal places. b. Determine the original population P 0 . Round to the nearest thousand. c. Determine the time required for the population to reach 300 , 000 . Round to the nearest hour.
Solution Summary: The author calculates the constant k to 3 decimal places for the model P(t)=P_0ekt.
The population
P
t
of a culture of bacteria grows exponentially for the first
72
hr
according to the model
P
t
=
P
0
e
k
t
.
The variable
t
is the time in hours since the culture is started. The population of bacteria is
60
,
000
after
7
hr
.
The population grows to
80
,
000
after
12
hr
.
a. Determine the constant
k
to
3
decimal places.
b. Determine the original population
P
0
. Round to the nearest thousand.
c. Determine the time required for the population to reach
300
,
000
. Round to the nearest hour.
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