Question

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication. At this rate of decay, how many bacteria will there be in 8 hours?

Answer 1

Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

$P(t) = P(0)(1-r)^{t}$

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that $P(0) = 750000, P(48) = 250$

We use this to find r. So

$P(t) = P(0)(1-r)^{t}$

$250 = 750000(1-r)^{48}$

$(1-r)^{48} = \frac{250}{750000}$

$\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}$

$1-r = 0.84637$

So

$P(t) = 750000(0.84637)^{t}$

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

$P(56) = 750000(0.84637)^{56} = 65.83$

Rounding to the nearest number

There will be 66 bacteria in 8 hours.