Respuesta :
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.
[tex]P(t) = P(0)(1-r)^{t}[/tex]
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 [tex]P(0) = 750000, P(48) = 250[/tex]
We use this to find r. So
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]250 = 750000(1-r)^{48}[/tex]
[tex](1-r)^{48} = \frac{250}{750000}[/tex]
[tex]\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}[/tex]
[tex]1-r = 0.84637[/tex]
So
[tex]P(t) = 750000(0.84637)^{t}[/tex]
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).
[tex]P(56) = 750000(0.84637)^{56} = 65.83[/tex]
Rounding to the nearest number
There will be 66 bacteria in 8 hours.
Answer:
197,488
Step-by-step explanation:
This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.
Identify the variables in the formula.
AA0ktA=250=750,000=?=48hours=A0ekt
Substitute the values in the formula.
250=750,000ek⋅48
Solve for k. Divide each side by 750,000.
13,000=e48k
Take the natural log of each side.
ln13,000=lne48k
Use the power property.
ln13,000=48klne
Simplify.
ln13,000=48k
Divide each side by 48.
ln13,00048=k
Approximate the answer.
k≈−0.167
We use this rate of growth to predict the number of bacteria there will be in 8 hours.
AA0ktA=?=750,000=ln13,00048=8hours=A0ekt
Substitute in the values.
A=750,000eln13,00048⋅8
Evaluate.
A≈197,488.16
At this rate of decay, researchers can expect 197,488 bacteria.
