# Thread: another exponential world problem

1. ## another exponential world problem

The accompanying table shows the number of milligrams, y, of a dose of a cold medication that remains in the body x hours after the dose has been ingested.

x(hrs) 2, 3, 5, 7, 9
y(mg) 11, 6.7, 2.9, 1.5, 0.9

Determine an exponential function y=ax^b that best fits the given data. Then estimate constants a and b to the nearest tenth. Find to the nearest minute when the amount of the drug that remains in the body first falls below 0.5 milligram.

2. Originally Posted by cityismine
The accompanying table shows the number of milligrams, y, of a dose of a cold medication that remains in the body x hours after the dose has been ingested.

x(hrs) 2, 3, 5, 7, 9
y(mg) 11, 6.7, 2.9, 1.5, 0.9

Determine an exponential function y=ax^b that best fits the given data. Then estimate constants a and b to the nearest tenth. Find to the nearest minute when the amount of the drug that remains in the body first falls below 0.5 milligram.
$\displaystyle y = ax^b$
$\displaystyle ln(y) = ln(ax^b)$
$\displaystyle ln(y) = b \cdot ln(x) + ln(a)$