Answer:
a) k = 0.0001245 /year
b) The Shroud of Turin is 757.52 years old.
Step-by-step explanation:
a) dC/dt = - KC
dC/C = - kdt
Integrating the left hand side from C₀ to C₀/2 and the right hand side from 0 to t(1/2) (where t(1/2) is the radioactive isotope's half life)
In [(C₀/2)/C₀] = - k t(1/2)
In (1/2) = - k t(1/2)
- In 2 = - k t(1/2)
k = (In 2)/t₍₁,₂₎
t(1/2) is given in the question to be 5566 years
k = (In 2)/5566 = 0.0001245 /year
b) dC/C = - kdt
Integrating the left hand side from C₀ to C and the right hand side from 0 to t
In (C/C₀) = - kt
C/C₀ = e⁻ᵏᵗ
C = C₀ e⁻ᵏᵗ
When C = 91% of C₀ = 0.91 C₀, solve for t
0.91 C₀ = C₀ e⁻ᵏᵗ
0.91 = e⁻ᵏᵗ
e⁻ᵏᵗ = 0.91
- kt = In 0.91 = -0.00943
t = - 0.00943/(-0.0001245) = 757.52 years.
Answer:
(1, 375) , (2, 375) , (3, 375) ...
Step-by-step explanation:
The function is defined by the rule:
f(x + 1) = f(x)
The first term of the sequence is 375. This means f(1) = 375
Lets find next few terms of the sequence. Replacing x by 1, we get:
f(1 + 1) = f(1)
f(2) = f(1)
f(2) = 375
Replacing x by 2, we get:
f(2 + 1) = f(2)
f(3) = f(2)
f(3) = 375
This shows, all the terms of the sequence are same and equal to 375. So the graph of the sequence would be a straight(horizontal) line as shown below. In ordered pairs the sequence would be represented as:
(1, 375) , (2, 375) , (3, 375) ...
Answer:
5 10 15 20 25 30 this one is the largest interquartile range