The bacterium Pseudomonas aeruginosa is cultured with an initial population of 10 4 active organisms. The population of active bacteria increases up to a point, and then due to a limited food supply and an increase of waste products, the population of living organisms decreases. Over the first 48 hr, the population P ( t ) can be approximated by: P ( t ) = − 1718.75 t 2 + 82 , 500 t + 10 , 000 where ? 0 ≤ t ≤ 48 a .Find the time required for the population to reach its maximum value. b .What is the maximum population?
The bacterium Pseudomonas aeruginosa is cultured with an initial population of 10 4 active organisms. The population of active bacteria increases up to a point, and then due to a limited food supply and an increase of waste products, the population of living organisms decreases. Over the first 48 hr, the population P ( t ) can be approximated by: P ( t ) = − 1718.75 t 2 + 82 , 500 t + 10 , 000 where ? 0 ≤ t ≤ 48 a .Find the time required for the population to reach its maximum value. b .What is the maximum population?
Solution Summary: The author explains how to calculate the maximum population of a bacterium by using the ti-83 calculator.
The bacterium Pseudomonas aeruginosa is cultured with an initial population of
10
4
active organisms. The population of active bacteria increases up to a point, and then due to a limited food supply and an increase of waste products, the population of living organisms decreases. Over the first 48 hr, the population
P
(
t
)
can be approximated by:
P
(
t
)
=
−
1718.75
t
2
+
82
,
500
t
+
10
,
000
where ?
0
≤
t
≤
48
a.Find the time required for the population to reach its maximum value.
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