A bacteria culture starts with 880 bacteria and grows at a rate proportional to its size. after 5 hours there will be 4400 bacteria. (a) express the population after t hours as a function of t. population: (function of t) (b) what will be the population after 2 hours? (c) how long will it take for the population to reach 2550?

Don't know whether or not you've encountered differential equations yet, but will try that approach here.

The growth rate is dy/dt = ky (which states that the rate is proportional to the size of the population, y, and k is a constant.

Grouping like terms,

dy

- - - = kt, so y = Ne^kt

y

We are told that at t=0, there are 880 bacteria. Thus, 880=N. Therefore,

y = 880e^ (kt). After 5 hours the pop will be 4400; using this info, find k:

4400=880e^ (5k), or 5 = e^ (5k). So, our y = 880e^ (kt) becomes

y = 880e^ (5t).

What will be the pop after 2 hours? y (2) = 880e^ (10) = 880 (22026) =

approx. 19,383,290 bacteria

Time to reach a pop of 2550? 2550 = 880e^ (5t). Find t.

ln 2550 = ln 880 + 5t, so ln 2550 - ln 880 = 5t. Divide both sides by 5 to obtain this time, t.