Question

An acidophilus culture containing 150 bacteria doubles in population every hour. (a) Write a function representing the bacteria population for every hour that passes. (b) Graph the function. (c) Use the graph to predict the number of bacteria after 12 hours.

Answer 1

Doubling every hour:
After 12 hours of acidophilus culture
150 bacteria turn into
150*2^12 or
614,400 bacteria after 12 hrs

Obviously I cant graph the function. Sorry.

Answer 2

A simple way (but not the absolute best way) to state the formula would be:
\[\huge{f(t) = (150)2^{t}}\]The more formal and generally-accepted way is to convert the base of "2" to "e":\[\huge{f(t) = (150)e ^{0.693147t}}\]

Answer 3

Here's a nice graph

Answer 4

In 12 hours:\[\huge{f(12) = (150)2^{12} = 614400}\]

Answer 5

This is what it looks like in 12 hours on the graph: