a culture started with 3,000 bacteria after 5 hours, it grew 3,900. bacteria. predict how many bacteria will be present after 9 hours. eound your answer to the nearet whole number.

P=Ae^kt

Question

a culture started with 3,000 bacteria after 5 hours, it grew 3,900. bacteria. predict how many bacteria will be present after 9 hours. eound your answer to the nearet whole number.

          P=Ae^kt

anonymous · Answer

Hm... I actually thought of this as a exponential funtions?

anonymous · Answer

its exponential growth

anonymous · Answer

hurry pleaseee i need help last question!!!

anonymous · Answer

OHHHHH i remember this. okay, so, any ideas

anonymous · Answer

Use P(0) find the value of A
Then plug P(5) and find the value of K
now u have your function P complete
Just plug the P(9) and there you go

anonymous · Answer

so what ? 
srry confused i really need help like this is the last question

anonymous · Answer

I don't really know, this is just a guess, but 5,400 bacteria, maybe?

anonymous · Answer

$$P(x)=Ae^{kt}$$ this is the equation that models the population of bacteria
We have as initial data that we started with 3000 bacteria, this means $$P(0)=3000$$
If we calculate $$P(0)=A{e}^{k(0)}=A=3000$$ we are able to find the value of A.
Problem also says that after 5 hours, bacteria population is 3900 which is $$P(5)=3900$$

Evaluating t=5 on our main equation we would have
$$P(5)=3000{e}^{5k}=3900$$
Solving this equation for k
$${e}^{5k}=1.3$$
$$\ln {e}^{5k}=\ln 1.3$$
$$5k=\ln 1.3$$
$$k=\frac{ \ln 1.3 }{ 5 }$$
We just found the value of k

So our main equation should be
$$P(t)=3000{e}^{\frac{ \ln1.3 }{ 5 }t}$$

So if we want to know what's the population of bacteria after 9 hours, we just evaluate t=9 in the equation
$$P(9)=3000{e}^{\frac{ \ln 1.3 }{ 5 } (9)}=4810.8$$ which is roughly 4810 bacteria