Question

the population of bacteria in a culture can be modeled by $p(t)=-0.01t^{3}+12.96t + 10$, where $t$ is the time in hours after the culture was started and $p(t)$ is the population in thousands. population of bacteria versus time part: 0 / 2 part 1 of 2 (a) evaluate $p(0)$ and $p(13)$ and interpret their meaning in the context of this problem. $p(0)=10$ means that the initial population of the bacteria in the culture was. $p(13)=$ try again that the 13 hr after the culture was started, bacteria were present.

Explanation:

Step1: Evaluate $P(0)$

Substitute $t = 0$ into $P(t)=-0.01t^{3}+12.96t + 10$.
$P(0)=-0.01(0)^{3}+12.96(0)+10=10$. This means that the initial population of the bacteria in the culture was $10$ thousand.

Step2: Evaluate $P(13)$

Substitute $t = 13$ into $P(t)=-0.01t^{3}+12.96t + 10$.
$P(13)=-0.01(13)^{3}+12.96(13)+10$.
First, calculate $(13)^{3}=2197$, then $-0.01(13)^{3}=-0.01\times2197=-21.97$.
Next, $12.96(13)=168.48$.
So $P(13)=-21.97 + 168.48+10=156.51$. This means that $13$ hours after the culture was started, $156.51$ thousand bacteria were present.

Answer:

$P(0) = 10$ means that the initial population of the bacteria in the culture was $10$ thousand.
$P(13)=156.51$ means that $13$ hr after the culture was started, $156.51$ thousand bacteria were present.