/sci/ - Science & Math

[Anonymous No.1970825]

ive been working on this damn problem for over 2 hours.

i need to write this shit as a function of t.


A bacteria culture starts with 440 bacteria and grows at a rate proportional to its size. After 6 hours there will be 2640 bacteria.
(a) Express the population after t hours as a function of t.

im so stuck and ragin hard.

ive gotten it to:

6k = ln(2640/440)

[Anonymous No.1970833]

bump ;_;

[Anonymous No.1970858]

[Troll Fucker No.1970873]

show me the setup and I can solve it for you

[Anonymous No.1970877]

dx/dt = kx
1/kx dx = 1 dt
(1/k)ln x = t
ln x = kt
x = ce^kt

That was extremely obvious, but I thought I'd show you how to do it just in case it wasn't obvious to you. c is 440, because e^0 = 1... And for the other value:

2640 = 440e^(6k)
6 = e^(6k)
ln 6 = 6k
k = (ln 6)/6

<span class="math">x = 440e^{\frac{(t)(\ln 6)}{6}}[/spoiler]

[Anonymous No.1970883]

>>1970873
back of the book had a very similar problem except k=1.
P(t)=Poe^(kt)

similar problem was 100(4.2)^t

[Anonymous No.1970906]

>>1970877
ty.

i was turning ln(6)/6 into 1. the dividing by 6 got my tripped up.
the face that i knew it was so damn easy is why it drove me up the fucking wall.

[Troll Fucker No.1970922]

A = 440*e^(0.29863*t) is the working function.