Answer:
To solve this problem, we can use a system of equations.
We know the quadratic expression has the form
Using points (1,12) and (4,0), we can form the following system to find a and b.
We need to divide the second equation by -4 and sum both equations
Then, we use this value to find the other variable
<h3>Therefore, the quadratic function that models the situation is</h3>
or 
According to this expression, after 2 seconds, the height is 16 feet.
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
Learn more about exponential growth;brainly.com/question/13674608
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Answer:
11%
Step-by-step explanation:
The full circle graph represents 100% of the given population. All populations are given except for "three or more." Adding all percentages of each population should add up to 100%.
No absences (none): 23%
One absence: 45%
Two absences: 21%
Three more absences: unknown.
Let the variable x represent the unknown population.
23% + 45% + 21% + x = 100%
Combine like terms.
89% + x = 100%
Subtract 89% from both sides.
x = 11%
To put it more simply, subtract all the percentages from 100% to get the percent of the missing population. 100 - 23 - 45 - 21 = 11
Answer:
-18, |-17|, |-18|, |19|, 20
Step-by-step explanation:
the absolute value of -17 is 17, the absolute value of -18 is 18, and the absolute value of 19 is just 19. Absolute values are never negative.
Hope this helps!
Is it obvious the 10% of the book's price is the $5 right?
So the book's price is $50.
