Answer:
![{7a^{5}b^{5} c\\](https://tex.z-dn.net/?f=%7B7a%5E%7B5%7Db%5E%7B5%7D%20c%5C%5C)
Step-by-step explanation:
![\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B28a%5E%7B8%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7B4a%5E%7B3%7Dbc%5E%7B2%7D%20%20%7D)
→ First look at the first term of each expression and see if they can be simplified, and they can
![\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B7a%5E%7B8%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7Ba%5E%7B3%7Dbc%5E%7B2%7D%20%20%7D)
→ Now look at the a terms, since a larger one is at the top, you subtract
![\frac{7a^{5}b^{6} c^{3} }{bc^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B7a%5E%7B5%7Db%5E%7B6%7D%20c%5E%7B3%7D%20%20%7D%7Bbc%5E%7B2%7D%20%20%7D)
→ Now simplify the b and c terms
![{7a^{5}b^{5} c](https://tex.z-dn.net/?f=%7B7a%5E%7B5%7Db%5E%7B5%7D%20c)
Answer:
The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.
The function to represent the mass of the sample after t days is ![A(t) = 810(0.74)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20810%280.74%29%5Et)
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance is given by:
![A(t) = A(0)(1-r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281-r%29%5Et)
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Hourly rate of change:
Decreases 26% by day. A day has 24 hours. This means that
; We use this to find r.
![A(t) = A(0)(1-r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281-r%29%5Et)
![0.74A(0) = A(0)(1-r)^{24}](https://tex.z-dn.net/?f=0.74A%280%29%20%3D%20A%280%29%281-r%29%5E%7B24%7D)
![(1-r)^{24} = 0.74](https://tex.z-dn.net/?f=%281-r%29%5E%7B24%7D%20%3D%200.74)
![\sqrt[24]{(1-r)^{24}} = \sqrt[24]{0.74}](https://tex.z-dn.net/?f=%5Csqrt%5B24%5D%7B%281-r%29%5E%7B24%7D%7D%20%3D%20%5Csqrt%5B24%5D%7B0.74%7D)
![1 - r = (0.74)^{\frac{1}{24}}](https://tex.z-dn.net/?f=1%20-%20r%20%3D%20%280.74%29%5E%7B%5Cfrac%7B1%7D%7B24%7D%7D)
![1 - r = 0.9875](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.9875)
![r = 1 - 0.9875 = 0.0125](https://tex.z-dn.net/?f=r%20%3D%201%20-%200.9875%20%3D%200.0125)
The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.
Starts out with 810 grams of Element X
This means that ![A(0) = 810](https://tex.z-dn.net/?f=A%280%29%20%3D%20810)
Element X is a radioactive isotope such that its mass decreases by 26% every day.
This means that we use, for this equation, r = 0.26.
The equation is:
![A(t) = A(0)(1-r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281-r%29%5Et)
![A(t) = 810(1 - 0.26)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20810%281%20-%200.26%29%5Et)
![A(t) = 810(0.74)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20810%280.74%29%5Et)
The function to represent the mass of the sample after t days is ![A(t) = 810(0.74)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20810%280.74%29%5Et)
You can look up cymath.com it will work the problem out for you and show you the steps.
Answer:
2,3,4,5,6,7,8,9,10, that's it easy