Respuesta :
A virus takes approximately 20.6 days to triple its original population.
What is the formula of exponential growth?
"[tex]f(x)=ab^x[/tex],
where a is the initial value
b is the growth rate
x is time. "
For given question,
Suppose the function for the population growth is,
[tex]A(t)=A_0\times b^t[/tex] .........(1)
For t = 13, the population growth of virus would be,
[tex]\Rightarrow A(13)=A_0\times b^{13}[/tex] ..........(2)
But we have been given that a virus takes 13 days to double its original population.
[tex]\Rightarrow A(13)=2\times A_0[/tex] .........(3)
From (2) and (3),
[tex]\Rightarrow A_0\times b^{13}=2\times A_0\\\\\Rightarrow b^{13}=2\\\\\Rightarrow b=1.0548[/tex]
We need to find the number of days to triple its original population
[tex]\Rightarrow A(t)=3\times A_0[/tex] ...........(4)
From (1) and (4),
[tex]\Rightarrow A_0\times b^t=A_0 \times 3\\\\\Rightarrow (1.0548)^t=3\\\\\Rightarrow t=20.6[/tex]
Therefore, a virus takes approximately 20.6 days to triple its original population
Learn more about the exponential growth here,
https://brainly.com/question/11487261
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