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)
A. Equilateral because it says” same measure”
Answer:
1200d rops of red coloring
800 drops of blue coloring
Step-by-step explanation:
The first thing is to make your pints and gallons the same unit. Todo this multiply 50 (the total amount of gallons) by 8 (the number of pints in a gallon)
50*8=400
next, multiply the drops of coloring out.
To do this multiply 400 by 3 drops for red
400*3=1200
Then Multiply 400 by 2 for blue
400*2=800
Here is the graph i looked it up in google idk if it's right but good luck
