Answer:
The equation that will represent the number of grams present after n hours is ![A(n) = 150(0.85)^n](https://tex.z-dn.net/?f=A%28n%29%20%3D%20150%280.85%29%5En)
3.035 grams will be left one day from now.
Step-by-step explanation:
Exponential equation for the amount of a substance:
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, and t is the time period.
A radioactive isotope is decaying at a rate of 15% every hour.
This means that ![r = 0.15](https://tex.z-dn.net/?f=r%20%3D%200.15)
Currently there are 150 grams of the substance.
This means that ![A(0) = 150](https://tex.z-dn.net/?f=A%280%29%20%3D%20150)
Write an equation that will represent the number of grams present after n hours.
![A(n) = A(0)(1-r)^n](https://tex.z-dn.net/?f=A%28n%29%20%3D%20A%280%29%281-r%29%5En)
![A(n) = 150(1-0.15)^n](https://tex.z-dn.net/?f=A%28n%29%20%3D%20150%281-0.15%29%5En)
![A(n) = 150(0.85)^n](https://tex.z-dn.net/?f=A%28n%29%20%3D%20150%280.85%29%5En)
How much will be left one day from now?
One day is 24 hours, so this is A(24).
![A(24) = 150(0.85)^{24} = 3.035](https://tex.z-dn.net/?f=A%2824%29%20%3D%20150%280.85%29%5E%7B24%7D%20%3D%203.035)
3.035 grams will be left one day from now.