Bacteria have a doubling time of roughly 10 hours. A normal bacteria starting population would be approximately 10,000 bacteria per ml of fluid...I am not sure if I have done these questions correctly and would like some confirmation before I hand this in to be marked!
a.) Write an equation to model this exponential growth, with B(t) representing the number of bacteria per m; and t representing the time in hours.
I did this B=10,000(2^10)^n
I am not sure that this is correct?!
d = 10 hours
C = 10 000 bacteria
N(t) = 10 000(2)^(t/10) is your equation
yes, sure... what are these variables? d C and then N, I have never heard of this before? Can you please clarify just a tad? Thanks and much appreciation to you!
Looking at this again, I am sure that mine is right. Mine is the same as yours. The only difference is the variables, and I also didn't type out the last part of my solution where the 10 hours is placed over t...I was taught to use n where you use t. I am using B(t) because I was told to, in the question and in my notes. As for N(t) again I think it is just a variable thing. So thanks for confirming my answer! Much appreciation to you!
No, your equation is not correct you do need the n/10 the way anonomous had it for you.
Just test it with values, eg time = 10
Your equation would result in B = 10000(2^20) which would be ridiculous
the equation that anonymous has would give
N(10) = 10000(2^1) = 20000, the right answer
Your exponent variable has to be divided by the doubling period, which in this case is 10 hours
To model exponential growth of bacteria with a doubling time of 10 hours, we can start by understanding the concept of exponentiation. When something doubles, it means that its current value is multiplied by 2.
Let's define B(t) as the number of bacteria per mL of fluid at time t in hours. Since the doubling time is 10 hours, we can say that the number of bacteria at time t is twice the number of bacteria at time t - 10 hours.
Therefore, we can write the equation for exponential growth as:
B(t) = B₀ * 2^(t/10),
where B₀ represents the initial number of bacteria at time t = 0.
In your attempt, you correctly identified the initial number of bacteria as 10,000 per mL of fluid (B₀). However, the rest of the equation appears to have some errors. The correct equation should be:
B(t) = 10,000 * 2^(t/10).
Please use this equation for your calculations and further inquiries.