# Math Help - Bacteria Decay Help, Thank You in Advance

1. ## Bacteria Decay Help, Thank You in Advance

A bacteria culture starts with 140 bacteria and grows at a rate proportional to its size. After 5 hours there will be 700 bacteria.

Express the population after t hours as a function of t.
population:

I just don't really understand the wording and how it might look.
Thank you,

2. Originally Posted by alexiri33
A bacteria culture starts with 140 bacteria and grows at a rate proportional to its size. After 5 hours there will be 700 bacteria.

Express the population after t hours as a function of t.
population:

I just don't really understand the wording and how it might look.
Thank you,
since $\frac{dP}{dt} = kP$ ...

$P = P_0 e^{kt}$

3. Originally Posted by alexiri33
A bacteria culture starts with 140 bacteria and grows at a rate proportional to its size. After 5 hours there will be 700 bacteria.

Express the population after t hours as a function of t.
population:

I just don't really understand the wording and how it might look.
Thank you,
Any quantity which "grows at a rate proportional to its size" can be modelled exponentially as N = No x e^(kt)
where the variables are : N is the quantity and t is time.
No is the original quantity and k ic called the "Proportionality constant".