Answer:
y = 1.8(2/3)^x
Explanation:
You want an exponential function that models the amount of medication remaining after x hours if it is initially 1.8 mL and decreases by a factor of 1/3 each hour.
Exponential model
You are given the form ...
y = a·b^x
In this form, the value of 'a' is the initial amount of medication, 1.8 mL. The value of 'b' is the "growth factor", which is ...
growth factor = 1 + growth rate
The problem statement tells us the change in the amount of remaining medication is -1/3 times the amount remaining in the previous hour. That is, the growth rate is -1/3, and the growth factor is ...
growth factor = 1 + (-1/3) = 2/3
Now we know the values of 'a' and 'b', so we can write the equation as ...
y = 1.8·(2/3)^x
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