Grade 6 module 2 lesson 3 classwork 9/4 ÷ 3/4=
2 answers:
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Answer:
a). k = 2.0794
b).
c). 13107200 cells
d). rate of growth after 6 hours = 27255112
e). 4.76 hours
Step-by-step explanation:
From the formula of bacterial population,
Where = Bacterial population after time t
= Initial population
k = relative growth factor
t = duration or time
a). For cells
and cells
Time t = 20 minutes = hours
Now we plug in these values in the formula,
100 =
By taking natural log on both the sides of the equation,
k = 3ln(2) = 2.0794
b). To get the expression we will plug in the value of k in the formula.
Since k = 3ln(2)
Let y =
By taking natural log on both the sides of the equation,
lny =
lny = 3t(ln2)ln(e)
ln(y) = 3t(ln2)
ln(y) =
y =
Now our expression will be
c). Number of cells after t = 6 hours
d). We can get the rate of growth by finding derivative of the expression
=
Now
= 2.0794×13107200
= 27255112
e) From the given formula,
3t(ln2) = ln(20000)
t =
t = hours