Answer:
It takes 16 days to quadruple its population.
Step-by-step explanation:
The population of the virus can be represented by the following exponential function.
[tex]A(t) = A_{0}e^{rt}[/tex]
In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.
In this problem, we have that:
[tex]A(8) = 2A_{0}[/tex]
So, we use this to find the value of r.
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]2A_{0} = A_{0}e^{8r}[/tex]
[tex]e^{8r} = 2[/tex]
Applying ln to both sides
[tex]8r = 0.6931[/tex]
[tex]r = 0.0867[/tex]
How long will it take to quadruple its population?
This is t when [tex]A(t) = 4A_{0}[/tex]
[tex]A(t) = A_{0}e^{rt}[/tex]
[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]
[tex]e^{0.0867t} = 4[/tex]
Again we apply ln to both sides.
[tex]0.0867t = 1.39[/tex]
[tex]t = 16[/tex]
It takes 16 days to quadruple its population.
The number of days it takes to quadruple it's population is; 16days
According to the question;
Therefore;
8days = 2A.
We are required to determine how long it will take to quadruple it's population;
Let no. of days required = x days.
By cross multiplication; we have;
By dividing through by 2A; we have;
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