Answer:
Option A - \(y=50(0.85)^x\)
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 \(y=ab^x\)
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 , \(y=\frac{50}{2}=25\)
Substitute in the general form,
\(y=ab^x\)
\(25=50(b^4)\)
\(b=(\frac{1}{2})^{\frac{1}{4}}\)
\(b=0.85\)
Therefore, The exponential function form is \(y=50(0.85)^x\)
Hence, Option A is correct.
