Question

Cooling. The temperature $T$ (in ${ }^{\circ} \mathrm{C}$ ) of coffee at time $t$ minutes after its removal from the microwave is given by the equation $$ T=25+73 e^{-0.28 t} $$ Find the temperature of the coffee at each time listed. a. $t=0$ b. $t=10$ c. $t=20$ d. after a long time 

   Cooling. The temperature $T$ (in ${ }^{\circ} \mathrm{C}$ ) of coffee at time $t$ minutes after its removal from the microwave is given by the equation

$$
T=25+73 e^{-0.28 t}
$$


Find the temperature of the coffee at each time listed.
a. $t=0$
b. $t=10$
c. $t=20$
d. after a long time
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Precalculus: A Right Triangle Approach
Precalculus: A Right Triangle Approach
Ratti, McWaters,… 5th Edition
Chapter 4, Problem 104 ↓
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Cooling. The temperature $T$ (in ${ }^{\circ} \mathrm{C}$ ) of coffee at time $t$ minutes after its removal from the microwave is given by the equation $$ T=25+73 e^{-0.28 t} $$ Find the temperature of the coffee at each time listed. a. $t=0$ b. $t=10$ c. $t=20$ d. after a long time
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Cooling. The temperature T (in °C) of coffee at time t minutes after its removal from the microwave is given by the equation T = 25 + 73e^{-0.28t}. Find the temperature of the coffee at each time listed: a) t=0 b) t=10 c) t=20 d) after a long time.
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A cup of coffee has a temperature of 90°C when it is poured and allowed to cool in a room with a temperature of 20°C. After 1 minute, the temperature of the coffee is 85°C. Determine the temperature of the coffee at time t. How long must you wait until the coffee is 25°C? a) T(t)=? (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) b) You will have to wait approximately ____ minutes until the coffee is 30 degrees C.
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The temperature of a cup of coffee $t$ min after it is poured is given by $$T=70+100 e^{-0.0446 t}$$ a. What was the temperature of the coffee when it was poured? b. When will the coffee be cool enough to drink (say, $120^{\circ} \mathrm{F}$ )?

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Transcript

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00:01 Okay, in this question, a formula of temperature of a cup of coffee is given, that is capital t equals to 70 plus 100, e raised to the power negative 0 .0446 small t, where this t is the time in minutes after the coffee is poured in the cup.
00:21 Okay.
00:21 And now there are two parts of this question.
00:24 So part a, what was the temperature of the coffee when it was poured or we can say at t? to 0 what will the temperature okay so temperature will be 70 plus 100 e -raged to the power negative 0 .0 446 and the time is 0 so e -r -r -race to the power negative 0 it will be 1 so the time temperature will be 70 plus 100 and it will be 1 70 degree fahrenheit so this will be the answer of part a of this question and now part b that is what when will the coffee be cool enough to drink say 120 degree fahrenheit okay so the temperature is given 120 and we have to find out that time okay so now we will put t equals temperature equals to 120 here and we will find out the time t so in the formula 120 equals to 70 plus 100 e -raised to the power negative 0 .0446 small t that is time okay so here we have to find out this small t and now first of all we will subtract both sides of the equation by 70.
01:33 So 120 minus 70 that is 50 equals to 100, e -raged to the power negative 0 .0446 t.
01:40 Now we will divide both side of the equation by 100.
01:43 So here 50 divided by 100 that can be written.
01:45 Okay, first of all 50 divided by 100 equals to e -raise to the power negative 0 .046 -t...
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