qustion(4) 4. The temperature of a cup of coffee t minutes after it is poured is
ID: 2883407 • Letter: Q
Question
qustion(4)
4. The temperature of a cup of coffee t minutes after it is poured is given by T(t) = 72 +100e^0.0446t ,where T is measured in degrees Fahrenheit.
a) what was the temperature of the coffee when it was poured?
b) when will the coffee be cool enough to drink(say, 125 degrees)?
Qustion(5)
An amount of $25,000 is deposited in a bank that pays interest at the rate of at 7%/year compounded annually. What is the total amount on deposit at the end of 6 yr, assuming there are no deposits or withdrawals during those 6 yr?
What is the interest earned during that period of time?
Explanation / Answer
4) we have given T(t) = 72 +100e^(0.0446t)
a) we have given T0-Ts=100 and Ts=72
where T0 is initial temperature of a cup of coffee and Ts is the temperature of the surrounding
T0=Ts+100 =72+100=1720 F
the temperature of the coffee when it was poured is 1720 F
b) we have given T(t) = 72 +100e^(0.0446t)
125 =72 +100e^(0.0446t)
125-72=100e^(0.0446t)
53 =100e^(0.0446t)
e^(0.0446t) =53/100
-0.0446t =ln(53/100)
t=-ln(53/100)/0.0446
t=14.234 minutes
the coffee will be cool enough to drink after 14.234 minutes
5) we have given P=$25,000,r=7% and t=6 years,n=1 time
we know the compounded interest formula is
A=P(1+r/n)nt
A=25,000(1+0.07/1)6
=25,000(1.07)6
=37518.2587962
the total amount on deposit at the end of 6 yr is $37518.2587962
interest =A-P=37518.2587962-25,000 =12518.2587962
the interest earned during that period of time is 12518.2587962
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