Answer:
A) 1000
B) 500
C) 4 days
Step-by-step explanation:
A colony of bacteria decays so that the population t days from now is given by the function:
[tex]n(t) = 1000\left(\dfrac{1}{2}\right)^{\dfrac{t}{4}}[/tex]
To find the amount of bacteria present when t = 0, simply substitute t = 0 into the function:
[tex]n(0) = 1000\left(\dfrac{1}{2}\right)^{\dfrac{0}{4}}\\\\\\n(0) = 1000\left(\dfrac{1}{2}\right)^{0}\\\\\\n(0) = 1000\left(1\right)\\\\\\n(0)=1000[/tex]
Therefore, the amount of bacteria present when t = 0 is 1000.
To find the amount of bacteria present in 4 days, substitute t = 4 into the function:
[tex]n(4) = 1000\left(\dfrac{1}{2}\right)^{\dfrac{4}{4}}\\\\\\n(4) = 1000\left(\dfrac{1}{2}\right)^{1}\\\\\\n(4) = 1000\left(\dfrac{1}{2}\right)\\\\\\n(4)=\dfrac{1000}{2}\\\\\\n(4)=500[/tex]
Therefore, the amount of bacteria present in 4 days is 500.
Since 500 is half of 1000, and it takes 4 days for this to occur, it indicates that the half-life is 4 days.
