Calculus
posted by Bill .
The temperature of a cup of Starbucks coffee at time t (in minutes) is T(t)= 70 + c e^(kt) . Initially, the temperature of the coffee was 200 degrees F. Three minutes later, it was 180 degrees. When will the temperature of the coffee be 150 degrees F?
The back of the book says it is 8.7 minutes, but I can't figure out how to get that answer.
Thank you for your help.

t(0)=200=70+ce^0
solve for c (130)
then
t(3)=70+130e^k3=180
solve for k
e^k3=11o/130
k3=.167
k=.0557
150=70+130e^(..0557)
.0557t=.486
t=8.7 min 
Thank you so much.
Respond to this Question
Similar Questions

Calculus AB
You pour a cup of coffee. when its poured, it is 130 F above room temperature, so we will say that difference D=130 F. 3 minutes later, it has cooled to D=117 F above room temperature. As the coffee cools, the instantaneous rate of … 
Math
I know that I have to use log to solve, but I am having a hard time with the word problems. Please help Coffee is best enjoyed at a temperature of 121° F. A restaurant owner wants to discover the temperature T at which he should serve … 
Chemistry/Calorimetry
You buy coffee (200.0 ml) served in a styrofoam cup. You are up late working in a chemistry lab, and want to drink the coffee right away, but at 95.0 degrees C, it is too hot to drink. You like the temperature of your coffee to be … 
math grade 12
Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called to … 
science chemistry
Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called to … 
Calc
A cup of coffee at 90 degrees celsius is put into a 30 degree celsius room when t =0 . The coffee's temperature, f (t ) , is changing at a rate given by f '(t )=8(0 .8) t degrees celsius per minute, where t is in minutes. Estimate … 
calc
q 0 125 250 375 500 625 750 C'(q) 27 35 41 45 43 46 51 Give fixed cost = 8800 and cost of producing 250 units is 17425, how much would the total cost increase if production were increased one unit, to 251 units? 
algebra
A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 65°F. The temperature of the coffee after t minutes is given by T(t) = 65 + 115e^−0.042t.(a) Find the temperature, to the nearest degree, … 
math
A cup of coffee at 173 degrees is poured into a mug and left in a room at 72 degrees. After 6 minutes, the coffee is 137 degrees. Assuming that Newton's Law of Cooling applies: After how many minutes will the coffee be 100 degrees? 
calculus
The differential equation below models the temperature of a 87°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 67°C. Solve the differential equation to …