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Masja [62]
3 years ago
9

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours. At this rate of decay,

Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

9,942 bacteria were there at 10 hours.

Step-by-step explanation:

Equation for population decay:

The equation for population decay, after t hours, is given by:

P(t) = P(0)(1-r)^t

In which P(0) is the initial population and r is the decay rate, as a decimal.

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.

This means that P(0) = 200000 and that when t = 18, P(t) = 900. So we use this to find r.

P(t) = P(0)(1-r)^t

900 = 200000(1-r)^{18}

(1-r)^{18} = \frac{900}{200000}

\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}

1 - r = (\frac{900}{200000})^{\frac{1}{18}}

1 - r = 0.7407

So

P(t) = P(0)(1-r)^t

P(t) = 200000(0.7407)^t

At this rate of decay, how many bacteria was there at 10 hours?

This is P(10). So

P(10) = 200000(0.7407)^{10} = 9941.5

Rounding to the nearest whole number:

9,942 bacteria were there at 10 hours.

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