Answer:
Q(t) = Q_o*e^(-0.000120968*t)
Step-by-step explanation:
Given:
- The ODE of the life of Carbon-14:
Q' = -r*Q
- The initial conditions Q(0) = Q_o
- Carbon isotope reaches its half life in t = 5730 yrs
Find:
The expression for Q(t).
Solution:
- Assuming Q(t) satisfies:
Q' = -r*Q
- Separate variables:
dQ / Q = -r .dt
- Integrate both sides:
Ln(Q) = -r*t + C
- Make the relation for Q:
Q = C*e^(-r*t)
- Using initial conditions given:
Q(0) = Q_o
Q_o = C*e^(-r*0)
C = Q_o
- The relation is:
Q(t) = Q_o*e^(-r*t)
- We are also given that the half life of carbon is t = 5730 years:
Q_o / 2 = Q_o*e^(-5730*r)
-Ln(0.5) = 5730*r
r = -Ln(0.5)/5730
r = 0.000120968
- Hence, our expression for Q(t) would be:
Q(t) = Q_o*e^(-0.000120968*t)
The answer is 30. 6 x 5 = 30. Please mark me Brainiest
A graph of the equation shows the appropriate choice to be
C. 2_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 =
24When the discriminant is
positive, the function has
two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).
<h3>
Answer: 6 dollars per kilogram</h3>
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Explanation:
The mixed number 4 & 1/2 converts to the decimal form 4.5
The unit price is 27/(4.5) = 6 dollars per kilogram
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If you wanted, you can think of it like this ratio
4.5 kg : 27 dollars
Dividing both parts of that ratio by 4.5 will lead to
1 kg : 6 dollars