Avat with 200 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 2 gal/min and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour? (round the answer to one decimal place.)

The percentage of alcohol after an hour is 4.8% (rounded to one decimal place)

Step-by-step explanation:

The vat initially has 200 gallons of beer with 4% alcohol by volume. 2gal/min of alcohol is added (containing 6% alcohol) for an hour.

STEP 1: FINDING THE TOTAL VOLUME OF BEER IN THE VAT

The volume of beer containing (containing 6% alcohol) after an hour = 2 * 60 = 120 gallons of beer.

The total volume of beer in the vat after an hour = 200 gal + 120 gal = 320 gal

STEP 2: FINDING THE TOTAL VOLUME OF ALCOHOL IN THE BEER AFTER AN HOUR

The volume of alcohol in the initial beer = 4/100*200 = 8 gal

The volume of alcohol in the beer being added at a constant rate = 6/100*120 = 7.2 gal

The total volume of alcohol in the vat after an hour = 8 gal + 7.2 gal = 15.2 gal

STEP 3: FINDING THE PERCENTAGE OF ALCOHOL AFTER AN HOUR

%of alcohol after an hour = total volume of alcohol in the beer after an hour /total volume of beer in the vat after an hour *100%

%of alcohol after an hour = 15.2/320*100% = 0.0475 * 100%

=4.75% = 4.8% (rounded to one decimal place)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0