Question

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 4 hours there will be 640 bacteria.
(a) Express the population after t hours as a function of t.

Answer 1

I got y=160 e^(t(In3.75/4))

Answer 2

) What will be the population after 5 hours?
i entered 5 into T

Answer 3

\[y=Ce^{kt}\]
You're told that \(C=160\), and that at \(t=4\) the population is 640. So, you have the equation
\[640=160e^{4k}\Rightarrow k=\frac{\ln2}{2}\]

Answer 4

so my equation was wrong....

Answer 5

how did you get this..?

Answer 6

it says i have to write equation : function of t)

Answer 7

\[640=160e^{4k}\\
4=e^{4k}\\
\ln4=4k\\
\frac{\ln4}{4}=k\\
\frac{\ln2^2}{4}=k\\
\frac{2\ln2}{4}=k\\
k=\frac{\ln2}{2}\]

Answer 8

For part a, you need to find the value of k. After that, you'll have both C and k, which you'll replace in the first equation I wrote:
\[\large y(t)=160e^{\frac{\ln2}{2}t}\]
Then use this to find the population at t = 5, i.e. \(y(5).\)

Answer 9

wht its become 4=e^4k?

Answer 10

\(640\div160=4\)

Answer 11

Oh I see haha the hardest one is the last question
c) How long will it take for the population to reach 1290 ?
Do i solve for t?

Answer 12

1290=160e(in2/2)(t)?

Answer 13

Yeah, that's it. Just make sure you know ln(2)/2 * t is in the exponent.