Answer:
430 minutes total
Step-by-step explanation:
Mo had 35 minutes sessions 14 times. You have to multiply 35 by 14 to get the answer which is 430 minutes.
Using a calculator, the slope of the line of best-fit is of 7.2.
<h3>How to find the equation of linear regression using a calculator?</h3>
To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows:
(-4,-32), (-2,-8), (0,10), (2,8), (4,32).
Using the calculator, the equation is:
y = 7.2x + 2.
Hence the slope is of 7.2.
More can be learned about a line of best-fit at brainly.com/question/22992800
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Slope intercept form is
, where 'm' is the slope and 'b' is the y-intercept.
Subtract 6x to both sides:
Divide 5 to both sides:
From the calculation, the growth rate is 0.88.
<h3>What is the growth rate?</h3>
To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
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