(a) Assuming that Q satisfies the differential equation Q' = -rQ, determine the decay constant r for carbon-14. (b) Find an expression for Q(t) at any time t, if Q(0) = Qo. (c) Suppose that certain remains are discovered in which the current residual amount of carbon-14 is 20% of the original amount. Determine the age of these remains.
Answer:
a) r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121/year
b) Q(t) = Q₀ (e^-rt)
c) Are of the 20% remnant of Carbon-14 = 13301.14 years.
Step-by-step explanation:
Q' = -rQ
Q' = dQ/dt
dQ/dt = -rQ
dQ/Q = -rdt
Integrating the left hand side from Q₀ to Q₀/2 and the right hand side from 0 to t1/2 (half life, t1/2 = 5730 years)
In ((Q₀/2)/Q₀) = -r(t1/2)
In (1/2) = -r(t1/2)
In 2 = r(t1/2)
r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121 /year
b) Q' = -rQ
Q' = dQ/dt
dQ/dt = -rQ
dQ/Q = -rdt
Integrating the left hand side from Q₀ to Q(t) and the right hand side from 0 to t.
In (Q(t)/Q₀) = -rt
Q(t)/Q₀ = e^(-rt)
Q(t) = Q₀ (e^-rt)
c) Q(t) = Q₀ (e^-rt)
Q(t) = 0.2Q₀, t = ? and r = 0.000121/year
0.2Q₀ = Q₀ (e^-rt)
0.2 = e^-rt
In 0.2 = -rt
-1.6094 = - 0.000121 × t
t = 1.6094/0.000121 = 13301.14 years.
Hope this Helps!
Answer:
Step-by-step explanation:
y & x
y = kx
When y = 6 , x = 72
6 = 72k
k = 6/72
k = 1/12
:- y = x/12
When x = 8
y = 8/12
y = 2/3
Answer:
1 2/8 inches
Step-by-step explanation:
smallest = 2/8
largest = 1 4/8
difference = 1 2/8
Answer:
<u>144</u>
Step-by-step explanation:
Ok. I love problems like this.
You just have to find the surface are of each part and add it up!
To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).
<u>Left rectangle:</u> 3*ll=33
<u>Middle rectangle:</u> 4*ll=44
<u>Right rectangle:</u> 5*ll=55
<u>Top triangle:</u> 3*4=12
12/2=6
<u>Bottom triangle:</u> 3*4=12
12/2=6
<u>ADD THEM ALL!!!</u> 33+44+55+6+6=<u>144</u>
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(Also can I please please please have brainliest? I need it to level up!)
Answer:
That's must be really cold!
