Respuesta :
5242880 insects would be present in 20 days.
The correct answer is an option (c)
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]
A colony of insects doubles every day.
⇒ b = 2
The colony has 5 insects today.
⇒ [tex]A_0=5[/tex]
So, the exponential growth function would be,
[tex]A(t)=5\times 2^t[/tex] ...........(1)
We need to find the number of insects after 20 days,
From equation (1),
[tex]\Rightarrow A(20)=5\times 2^{20}\\\\\Rightarrow A(20)=5\times 1048576\\\\\Rightarrow A(20)=5242880[/tex]
Therefore, 5242880 insects would be present in 20 days.
The correct answer is an option (c)
Learn more about the exponential growth here,
brainly.com/question/11487261
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