Question #b1d2e

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Answer 1 · 2017-01-21T21:53:35

#2, 048,000# bacteria

We can say straightaway that

#B(t) = B_o * 2^(t/0.25)#

To check this:

To start with: #B(0) = B_o * 2^(0) = B_o#
Then: #B(0.25) = B_o * 2^(0.25/0.25) = 2 B_o# so it is doubling :)
And: #B(0.50) = B_o * 2^(0.50/0.25) = 4 B_o#, so it has quadrupled. The pattern is established.

Now, if at time 1.25 hours, there are 40,000 bacteria present, we can say that:

#40,000 = B_o * 2^(1.25/0.25) = 5B_o implies B_o = 8,000 #

So:

#color(blue)(B(t) = 8,000 (2)^(t/0.25))#

After 2 hours:

#B(2) = 8,000 * 2^(2.00/0.25)#

# = 8,000 * 2^(8) = 2, 048,000#