Word Problem - Sorry I am new!

[jaredroy23]

Hi. I'm new. Can someone help me with this word problem?

The E. coli bacteria are found in humans. Suppose that 3000 of the bacteria are present at time t = 0. If N is the number of bacteria present in the bloodstream at any time t, in minutes and N(t) = 3000(2) ^t/20, how many bacteria will be present after 40 minutes?

I have done this a few different ways and I have gotten 3 different answers:

24,000
48,000
96,000

So I am not sure if i am doing anything right. Please help.

Thanks Jared

 

[soroban]

Hello, jaredroy23!

The E. coli bacteria are found in humans.
Suppose that 3000 of the bacteria are present at time t = 0.
If \(\displaystyle N\) is the number of bacteria present in the bloodstream at any time \(\displaystyle t\) in minutes,
and \(\displaystyle N(t)\,=\,3000\cdot2^{\frac{t}{20}}\),
how many bacteria will be present after 40 minutes?

I have done this a few different ways and I have gotten 3 different answers:
. . 24,000 . . 48,000 . . 96,000
. . . . . "a few different ways"? . very imaginative! . . . . and all wrong!

Just plug in \(\displaystyle t\,=\,40\)

\(\displaystyle f(40)\:=\:3000\cdot2^{(\frac{40}{20})}\:=\:3000\cdot2^2\:=\:3000\cdot4\;=\;12,000\)