Question

Elizabeth is a nurse, and she just administered 1.8 milliliters of medication to one of her patients. Elizabeth knows that the amount of medication remaining in the patient's body will decrease by a factor of 1 3 each hour.

Answer 1

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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