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Yuki888 [10]
3 years ago
12

The population P of a colony of 3600 bacteria at time t minutes can be modeled by the function P(x) = 3600(2)^t/73. How long doe

s it take the population (in hours) to reach 1,792,000?

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
8 0
It takes 10.9 hours.

We set the equation equal to 1792000:

1792000=3600(2)^{\frac{t}{73}}

Divide both sides by 3600:
\frac{1792000}{3600}=\frac{3600(2)^{\frac{t}{73}}}{3600}
\\
\\\frac{4480}{9}=2^{\frac{t}{73}}

We will use logarithms to solve this:
\log_2{\frac{4480}{9}}=\frac{t}{73}

Multiply both sides by 73:
73\log_2{\frac{4480}{9}}=t
\\
\\654.03=t

This is in minutes; to convert to hours, divide by 60:
654.03/60 = 10.9
ValentinkaMS [17]3 years ago
4 0
The answer is: 10.90 hours

Explanation:
Please see the image attached!

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