Respuesta :
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:
[tex]P(t) = P(0)(1-r)^t[/tex]
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 [tex]P(0) = 200000[/tex] and that when [tex]t = 18, P(t) = 900[/tex]. So we use this to find r.
[tex]P(t) = P(0)(1-r)^t[/tex]
[tex]900 = 200000(1-r)^{18}[/tex]
[tex](1-r)^{18} = \frac{900}{200000}[/tex]
[tex]\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}[/tex]
[tex]1 - r = (\frac{900}{200000})^{\frac{1}{18}}[/tex]
[tex]1 - r = 0.7407[/tex]
So
[tex]P(t) = P(0)(1-r)^t[/tex]
[tex]P(t) = 200000(0.7407)^t[/tex]
At this rate of decay, how many bacteria was there at 10 hours?
This is P(10). So
[tex]P(10) = 200000(0.7407)^{10} = 9941.5[/tex]
Rounding to the nearest whole number:
9,942 bacteria were there at 10 hours.
