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For many people suffering from constrictedbronchial muscles, the drug Albuterol is prescribed. The number of micrograms $A$ of Albuterol in a person's bloodstream $t$ minutes after 200 micrograms have been inhaled can be approximated by$$A=-50 t^{2}+200 t$$How long after an inhalation will there be about 150 micrograms of Albuterol in the bloodstream? Source: Based on information in Chohan, Naina, Rita M. Doyle, and Patricia Nayle (eds.), Nursing Handbook, 21st ed.

$1 \mathrm{min}, 3 \mathrm{min}$

Algebra

Chapter 6

Polynomial Factorizations and Equations

Section 7

Applications of Polynomial Equations

Graphs and Statistics

Exponents and Polynomials

Equations and Inequalities

Polynomials

Missouri State University

Campbell University

Harvey Mudd College

Lectures

01:13

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We're trying to find a time that 150 milligram micrograms of I'll be raw reaches the bloodstream after inhalation. So a is for Butera and we're trying to find when there's 100 for the micrograms in there. So we have 150 to replace A 150 equals negative 50 t squared plus 200 t now moving 132. What will gas you move this side This expression to the other side to make it easier to have the t squared coefficient positive. So we have 50 t squared because we know the other side minus 200 t plus 150 egos to zero. So now they all have a common factor of 50. So we factor out of 50 we have t squared minus 40 plus tree equals +20 dividing by 50 on both sides. Zero divided by five is zero. So we have teas squared minus forward t blustery. He goes to zero. Now we just have to factor. We used the X method it so we have t and T eights hind C, which is a coefficient here in the cold fusion here, which is just one times three. And in the court, fishing here goes again on the bottom, which is negative for So what times What? He goes to three. And what? Plus what goes to negative for seeing this is just gonna be negative. Three times. Negative one. This is positive. Negative three plus negative one Because negative for So therefore, we have t minus one and Time T minus 30 And now we have time if you go to one. And time is he was three.

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