document.write( "Question 1163608: cup of coffee at 85°C is placed in a freezer at 0°C.The temperature of the coffee decreases exponentially, so that after 5 minutes it is 30°C.
\n" ); document.write( "(a)What is its temperature after 3 minutes?
\n" ); document.write( "(b)Find by trial how long it will take for the temperature to drop ton5°C \n" ); document.write( "
Algebra.Com's Answer #787749 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
one of the formula that works best with these types of problem is:
\n" ); document.write( "f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present value
\n" ); document.write( "r is the interest rate per time period
\n" ); document.write( "n is the number of time periods.\r
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\n" ); document.write( "\n" ); document.write( "in your problem, the equation becomes:
\n" ); document.write( "30 = 85 * (1 + r) ^ 5
\n" ); document.write( "divide both sides of the problem by 85 and then take the fifth root of both sides of the equation to get:
\n" ); document.write( "(30/85)^(1/5) = 1 + r
\n" ); document.write( "subtract 1 from both sides of the equation to get:
\n" ); document.write( "(30/85)^(1/5) - 1 = r
\n" ); document.write( "solve for r to get:
\n" ); document.write( "r = -.1880290984
\n" ); document.write( "replace r with that in the original equation to get:
\n" ); document.write( "30 = 85 * (1-.1880290984) ^ 5 = 30, confirming the value of r is good.
\n" ); document.write( "now that you know r, you can solve the equation.
\n" ); document.write( "the equation becomes:
\n" ); document.write( "5 = 85 * (1-.1880290984) ^ n
\n" ); document.write( "divide both sides of the equation by 85 and take the log of both sides of the equation to get:
\n" ); document.write( "log(5/85) = log(1-.1880290984)^n)
\n" ); document.write( "since loc(x^a) = a * log(x), this equation becomes:
\n" ); document.write( "log(5/85) = n * log(1-.1880290984)
\n" ); document.write( "divide both sides by log(1-.1880290984) to get:
\n" ); document.write( "log(5/85)/log(1-.1880290984) = n
\n" ); document.write( "solve for n to get:
\n" ); document.write( "n = 13.60220271 minutes
\n" ); document.write( "it will take 13.60220271 minutes for the temperature to drop from 85 degrees to 5 degrees.
\n" ); document.write( "that was the answer to your question b.
\n" ); document.write( "the answer to your wuestion a follows.
\n" ); document.write( "after 3 minutes, the equation becomes:
\n" ); document.write( "f = 85 * (1-.1880290984)^3 = 45.50303066 degrees.
\n" ); document.write( "the equation can be graphed.
\n" ); document.write( "it is shown below:\r
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