Question

a dye is injected into the pancreas during a certain medical procedure. a physician injects 0.3 grams of the dye, and a healthy pancreas will secrete 4% of the dye each minute. predict the amount of dye remaining, to the nearest hundredth of a gram, in a healthy pancreas 30 minutes after the injection.

Answer 1

0.09 g

Explanation:

You want to know the amount remaining of 0.3 g of dye after 30 minutes if the amount decreases by 4% per minute.

Exponential function

The amount can be modeled by the exponential function ...

q = a·b^t

where q is the quantity remaining, 'a' is the initial quantity, b is the growth factor per minute, and t is the number of minutes.

The growth factor is related to the growth rate by ...

b = 1 + growth rate

Application

Here, the growth rate is -4% per minute, so the growth factor is ...

b = 1 +(-0.04) = 0.96

The initial quantity is 0.3 grams, so the remaining quantity after 30 minutes is ...

q = 0.30·0.96^30 ≈ 0.08816 ≈ 0.09 . . . . grams

The amount of dye remaining after 30 minutes is predicted to be 0.09 g.

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