# Help in math exploration !!!

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Hey everyone,

So I'm currently doing a practice math IA for maths SL and I need help! I chose the topic to do exponential growth and decay and I'm investigating the growth rate of bacteria however, I'm a little stuck. So basically, I've already got the formula for exponential growth of bacteria but that's pretty simple math and idk what else to do like do I just plug in numbers bc that's kinda boring and way too simple. I was thinking about investigating the effect of glucose-salt levels on E. coli bacteria to extend the topic but I don't really know how to do that and all the websites I've found go way too in-depth about the biology and not enough about the math. So please leave any useful websites or other for this kinda topic or any other idea on how I could extend my topic. All help is appreciated !!

Thank you!

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You can derive the formula for exponential growth/decay from solving a separable differential equation, which is, as far as I know, beyond SL but not that much beyond. It's definitely something to consider if you decide to do the real one on a similar topic. For the practice, you can graph ln (population at time t / initial population) vs time and apply linear regression to the data to find the growth/decay constant  (algebraically, what is this ln (pop at time t / initial pop)?) Then you can discuss some limitations to using linear regression on semilog plot (eg is it really minimizing the vertical differences, as what is expected from the linear regression formula). You can also discuss the benefits to finding a regression rather than using two points to find the growth/decay constants (eg systematic vs random errors).

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