A kilo means 1,000. there for there are always 1,000 grames in one kilo.
The half-life of the element is 13 minutes, which means after 13 minutes, any starting amount decays to half. So element X decays with a rate k such that
![\dfrac12 = e^{13k}](https://tex.z-dn.net/?f=%5Cdfrac12%20%3D%20e%5E%7B13k%7D)
Solve for k :
![\ln\left(\dfrac12\right) = \ln\left(e^{13k}\right)](https://tex.z-dn.net/?f=%5Cln%5Cleft%28%5Cdfrac12%5Cright%29%20%3D%20%5Cln%5Cleft%28e%5E%7B13k%7D%5Cright%29)
![-\ln(2) = 13k \ln(e)](https://tex.z-dn.net/?f=-%5Cln%282%29%20%3D%2013k%20%5Cln%28e%29)
![-\ln(2) = 13k](https://tex.z-dn.net/?f=-%5Cln%282%29%20%3D%2013k)
![\implies k = -\dfrac{\ln(2)}{13}](https://tex.z-dn.net/?f=%5Cimplies%20k%20%3D%20-%5Cdfrac%7B%5Cln%282%29%7D%7B13%7D)
Now, we solve for t such that
![36 = 710e^{kt}](https://tex.z-dn.net/?f=36%20%3D%20710e%5E%7Bkt%7D)
![e^{kt} = \dfrac{18}{355}](https://tex.z-dn.net/?f=e%5E%7Bkt%7D%20%3D%20%5Cdfrac%7B18%7D%7B355%7D)
![\ln\left(e^{kt}\right) = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=%5Cln%5Cleft%28e%5E%7Bkt%7D%5Cright%29%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![kt = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=kt%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![-\dfrac{\ln(2)}{13} t = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B%5Cln%282%29%7D%7B13%7D%20t%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![\implies t = -\dfrac{13 \ln\left(\frac{18}{355}\right)}{\ln(2)}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%20-%5Cdfrac%7B13%20%5Cln%5Cleft%28%5Cfrac%7B18%7D%7B355%7D%5Cright%29%7D%7B%5Cln%282%29%7D)
![\implies t = -13 \log_2\left(\dfrac{18}{355}\right) \approx \boxed{55.9}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%20-13%20%5Clog_2%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29%20%5Capprox%20%5Cboxed%7B55.9%7D)
Answer:
y=1/3x+4
Step-by-step explanation:
It should be correct as the gradient = 1/3
and the y-intercept = C
= +4
Answer:
A. y-intercept is 8, Slope is -4/3
Step-by-step explanation:
Set up a proportion:
2 x
-- = --
5 10.5
Then just solve for x