Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A bacteria culture is known to grow at a rate proportional to the amount present.After $1$ hour $1000$s stands of the bacteria are observed in the culture;and after $4 $years $3000$ strands. Find:

  1. an expression for the approximate number of strands of the bacteria present in the culture at any time $t$
  2. the approximately number of strands of the bacteria originally in the culture.
share|improve this question
Surely you have an idea about how to begin a solution... –  Did Jul 1 '12 at 22:17
Please try to avoid capslock titles, as they are perceived as though you are shouting. Second, the imperative tone of this post is not fitting the site, please edit it to make it slightly more polite. By the way, if this question is a homework assignment please add the [homework] tag to it. –  Asaf Karagila Jul 1 '12 at 22:17
What have you tried? What equation do you have for exponential growth? –  Ross Millikan Jul 1 '12 at 22:19

1 Answer 1

Fit the data to the model $s(t) = s_0 e^{\alpha t}$.

Let $t_1 = 1$ hour, $t_2 = 4$ years. You have $s(t_1) = 1000$, $s(t_2) = 3000$.

Then the model gives $s(t_i) = s_0 e^{\alpha t_i}$, $i \in \{1,2\}$.

From this you can easily estimate $\alpha$ using; $\frac{s(t_1)}{s(t_2)} = e^{\alpha (t_2-t_1)}$.

Given $\alpha$, it is straightforward to figure out $s_0$ using $s(t_1) = s_0 e^{\alpha t_1}$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.