Respuesta :
The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.
Step-by-step explanation:
The given is,
A new virus with a decay rate of 19% per hour
They start with 300 viruses
Step:1
Formula to calculate the viruses at decay rate,
[tex]y = A(1-r)^{t}[/tex]............................(1)
Where, y - No of viruses after given time
A - Viruses at initial stage
r - Decay rate
t - No. of hours
From the given,
A = 300
r = 19% per hour
t = 7 hours
Equation (1) becomes,
[tex]y = 300(1-0.19)^{7}[/tex]
[tex]= 300(0.81)^{7}[/tex]
[tex]= 300(0.228767)[/tex]
[tex]= 68.63[/tex]
Viruses of 7 hours ≅ 69 viruses
( or )
Step:1
For 1st hour,
= (No.of viruses in hour) - (No,of viruses in last hour × Decay rate )
= (300)-(300 × 0.19)
= 300 - 57
= 243
For 2nd hour,
= (243)-(243 × 0.19)
= 243 - 46.17
= 196.83
For 3rd hour,
= (196.83)-(196.83 × 0.19)
= 196.83 - 37.39
= 159.4323
For 4th hour,
= (159.4323)-(159.4323 × 0.19)
= 159.4323 - 30.2921
= 129.1402
For 5th hour,
= (129.1402)-(129.1402 × 0.19)
= 129.1402 - 24.5366
= 104.6035
For 6th hour,
= ( 104.6035)-( 104.6035 × 0.19)
= 104.6035 - 19.8747
= 84.7288
For 7th hour,
= (84.7288)-(84.7288 × 0.19)
= 84.7288 - 16.0984
= 68.63 viruses
Result:
The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.
Using an exponential function, it is found that they will find 69 viruses in 7 hours.
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem:
- Decay rate of 19% per hour, hence [tex]r = 0.19[/tex]
- They start with 300 viruses, hence [tex]A(0) = 300[/tex]
Then
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 300(1 - 0.19)^t[/tex]
[tex]A(t) = 300(0.81)^t[/tex]
In 7 hours:
[tex]A(7) = 300(0.81)^7 = 69[/tex]
They will find 69 viruses in 7 hours.
A similar problem is given at https://brainly.com/question/25537936
