Respuesta :
Answer:
157,286,400 bacteria.
Step-by-step explanation:
We have been given that a certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with.
We will use exponential growth function to solve our given problem.
[tex]y=a\cdot b^x}[/tex], where
y = Final value,
a = Initial value,
b = Growth factor.
x = Time.
Quadruples meaning 4 at a time, so growth factor is 4.
We are also told that population becomes 4 times every 6 hours, so time would be [tex]\frac{1}{6}x[/tex].
Initial value is given as 150.
Upon substituting these values in above formula, we will get:
[tex]y=150(4)^{\frac{1}{6}x}[/tex]
Let us convert two and a half days into hours.
1 day = 24 hours.
2.5 days = 2.5*24 hours = 60 hours.
To find the bacteria population in two and half days, we will substitute [tex]x=60[/tex] in our formula as:
[tex]y=150(4)^{\frac{1}{6}(60)}[/tex]
[tex]y=150(4)^{10}[/tex]
[tex]y=150(1048576)[/tex]
[tex]y=157,286,400[/tex]
Therefore, there will be 157,286,400 bacteria in two and a half days.
