Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
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In the given scenario, we have ...
So, our model is ...
p = 6000·1.1^(t/4)
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After 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
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Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
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In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
