<h3><u>Solution</u><u>:</u><u>-</u></h3>
(3/4)to the power of 3 in form of p/q
Exponential Growth
Some real-life events grow in such a way that they can be modeled as an exponential function, given as:
Where C(t) is the future value of the measured variable, Co is its initial value, r is the growth rate and t is the time.
We are given the following data:
Initial amount: Co=40 bacteria
Growth rate: 1 + r = 3
The bacteria triples every 4 days, thus t is the number of periods of 4 days.
Thus the model is:
We can solve the equation
1 + r = 3
And get r = 2. Rewriting the equation:
We are required to find the number of bacteria after 20 days, that is, after 20/4 = 5 periods of 4 days. Substituting:
Calculating:
The colony would have 9,720 bacteria after 20 days
Let x=large boxes and y=small boxes.
x+y=110
60x+35y=5100
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You need to cancel out one of the variables to solve for one. Let's cancel out y.
-35(x+y=110)
-35x-35y=-3850
60x+35y=5100
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Add the two equations.
25x=1250
x=50
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Plug in 50 for x into one of the equations to solve for y.
50+y=110
y=60
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50 large boxes
60 small boxes