Respuesta :
Answer:
Option A
Step-by-step explanation:
The complete question is attached here
The rate of increase of bacterial population be K
As we know
[tex]Y = Y_0 * e^{kT}[/tex]
where Y is the final population. In this case it is 1000
K is the rate of increase of population i.e 3 times per hour
T is the time in hours
Y0 is the initial population = 5
Substituting the given values, we get -
[tex]1000 = 5 *e^{3*T}\\200 = e^{3*T}[/tex]
Taking log on both sides, we get -
ln [tex]200[/tex] = ln [tex]e^{3T}[/tex]
[tex]2.718 * 2.301 = 3T[/tex]
T = 2.084 hours
hence, option A is correct
The number of hours required after the initial time must be divide the sample by John is 2.084 hours.
What is an exponential function?
Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a, b, and c are the real number
John needs to divide the sample in half once the number of bacteria has reached 1000.
The table of this bacterial growth is,
Time(hours) Number of bacteria
0 5
1 15
2 45
The rate of increasing the bacteria each hour is,
[tex]x=\dfrac{15}{5}=3\\x=\dfrac{45}{15}=3[/tex]
Thus, the exponential rate is 3.
Now the number of reached is 1000, and the initial population was 5. Therefore, for the time t, the exponential function can be given as,
[tex]1000=5e^{3t}\\\dfrac{1000}{5}=e^{3y}\\200=e^{3y}[/tex]
Taking log both the sides as,
[tex]\ln (200)=\ln e^{3t}\\2.301=0.434({3t})\\t=2.084[/tex]
Hence, the number of hours required after the initial time must be divide the sample by John is 2.084 hours.
Learn more about the exponential function here;
https://brainly.com/question/15602982
