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sp2606 [1]
3 years ago
6

When a bactericide is added to a nutrient broth in which bacteria are​ growing, the bacteria population continues to grow for a​

while, but then stops growing and begins to decline.
The size of the population at time t​ (hours) is b = 9^6 + 6^4t - 6^3t^2.
Find the growth rates at t = 0 hours, t = 3 hours, and t = 6 hours.
Mathematics
1 answer:
baherus [9]3 years ago
3 0

Answer:

a)  1296 bacteria per hour

b) 0 bacteria per hour

c) -1296 bacteria per hour

Step-by-step explanation:

We are given the following information in the question:

The size of the population at time t​ is given by:

b(t) = 9^6 + 6^4t-6^3t^2

We differentiate the given function.

Thus, the growth rate is given by:

\displaystyle\frac{db(t)}{dt} = \frac{d}{dt}(9^6 + 6^4t-6^3t^2)\\\\= 6^4-2(6^3)t

a) Growth rates at t = 0 hours

\displaystyle\frac{db(t)}{dt} \bigg|_{t=0}= 6^4-2(6^3)(0) = 1296\text{ bacteria per hour}

b) Growth rates at t = 3 hours

\displaystyle\frac{db(t)}{dt} \bigg|_{t=3}= 6^4-2(6^3)(3) = 0\text{ bacteria per hour}

c) Growth rates at t = 6 hours

\displaystyle\frac{db(t)}{dt} \bigg|_{t=6}= 6^4-2(6^3)(6) = -1296\text{ bacteria per hour}

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