Question

the population of bacteria in a culture can be modeled by ( p(t)=-0.01 t^{3}+12.96 t + 10 ), where ( t ) is the time in hours after the culture was started and ( p(t) ) is the population in thousands.

part: ( 0 / 2 )
part 1 of 2
(a) evaluate ( p(0) ) and ( p(12) ) and interpret their meaning in the context of this problem.
( p(0)=10 ) means that the population of the bacteria in the culture was 10.
( p(12)= ) means that the br after the culture was started, bacteria were present.

Explanation:

Step1: Evaluate \(P(0)\)

Substitute \(t = 0\) into \(P(t)=-0.01t^{3}+12.96t + 10\).
\(P(0)=-0.01\times(0)^{3}+12.96\times(0)+10=10\)

Step2: Evaluate \(P(12)\)

Substitute \(t = 12\) into \(P(t)=-0.01t^{3}+12.96t + 10\).

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Answer:

\(P(12) = 148.24\) means that the population \(12\) hours after the culture was started, \(148240\) bacteria were present (since \(P(t)\) is in thousands, \(148.24\times1000 = 148240\)).