SOLUTION: The temperature of a cooling liquid over time can be modeled by the exponential function
T(x)= 60(1/2)^x/30 + 20
where T is the temperature in degrees Celsius and x is the e
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T(x)= 60(1/2)^x/30 + 20
where T is the temperature in degrees Celsius and x is the e
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Question 1056037: The temperature of a cooling liquid over time can be modeled by the exponential function
T(x)= 60(1/2)^x/30 + 20
where T is the temperature in degrees Celsius and x is the elapsed time in minutes.
a) graph the function.
b) Determine how long it takes for the temperature to reach 28 degrees Celsius.
c) Check the accuracy of your answer with a TI-83 calculator
What I've got:
a) Making a graph with X as time and Y as Temperature. Going to plug random x values (5, 10, 15) into the formula to see what y values (temperature) I get. What else can I do?
b) I understand to isolate X. I subtract 20 to both sides to get 8= 60(1/2)^x/30 then divide both sides by 60 to get 8/60= (1/2)^x/30. But there I'm stuck. Someone suggested something about using a logarithim, but I'm not that far in the course yet and logarithims have not been taught yet. What's the next non-logarithim step(s)?
c) Have no clue how to configure the calculator to get an answer. Maybe once I finally solve B.
Any help is appreciated. Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! a) Yes but since the function is non-linear, you'll need more points.
You can also use an online graphing utility.
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b) You could then plot a line at and find the corresponding value. This graphing utility will do it automatically to three decimal places.
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c) Yes you can solve the equation,
Now you can use your calculator.
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