A certain culture of the bacterium Streptococcus A initially has 12 bacteria and is observed to double every 1.5 hours.
Estimate the number of bacteria after 26 hours.

Question

A certain culture of the bacterium Streptococcus A initially has 12 bacteria and is observed to double every 1.5 hours.
Estimate the number of bacteria after 26 hours.

anonymous · Answer

Is there an equation?

anonymous · Answer

$$n(t)=12*2^{t/1.5}$$

anonymous · Answer

I know 26 goes in for t but idk how to do the rest. thats my problem

anonymous · Answer

Are you working with a text book? If you are what is the answer?

anonymous · Answer

no im not. its online.

anonymous · Answer

Ok well when you put 26 into the equation it's in the exponent so we divide it by 1.5 so what do you get?

anonymous · Answer

$$17\frac{ 1 }{3 }$$

anonymous · Answer

$$n(26)=12*2^{17\frac{ 1 }{3 }}$$ ?

anonymous · Answer

Good Now notice that the 12 and the 2 are separate so the exponent - the answer we just got- will only be applied to the 2. So now put 2 to the power of $$17\frac{ 1 }{ 3 }$$

anonymous · Answer

What do you get?

anonymous · Answer

So... I got (165140.3719) now we multiply this by 12 to get our final answer which is 1981684.462 or (1.9 x 10^6)

anonymous · Answer

Hope this helped :)

anonymous · Answer

im loving you right now thank you :)

anonymous · Answer

so i didnt have to do anything with the n(26)?

anonymous · Answer

that was the part that messed me up