Answer:
Option A -
Step-by-step explanation:
Given : The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.
To find : Which function can be used to determine the approximate number of grams of the sample remaining after t hours?
Solution :
The general form of exponential is ![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
where a is the initial value , b is the growth or decay rate.
We have given initial value is 50 i.e, a=50
The half life of a certain substance is about 4 hours.
x=4 , ![y=\frac{50}{2}=25](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B50%7D%7B2%7D%3D25)
Substitute in the general form,
![y=ab^x](https://tex.z-dn.net/?f=y%3Dab%5Ex)
![25=50(b^4)](https://tex.z-dn.net/?f=25%3D50%28b%5E4%29)
![b=(\frac{1}{2})^{\frac{1}{4}}](https://tex.z-dn.net/?f=b%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![b=0.85](https://tex.z-dn.net/?f=b%3D0.85)
Therefore, The exponential function form is ![y=50(0.85)^x](https://tex.z-dn.net/?f=y%3D50%280.85%29%5Ex)
Hence, Option A is correct.