The temperature of a cooling liquid over time can be modelled by 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°C
c) Check the accuracy of your answer
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How do you graph a function? Make a table of points x and y : x = time and y = temperature.
Let T(x) = 28 and solve for x.
28 = 60(1/2)^(x / 30) + 20
8 = 60(1/2)^(x / 30)
2/15 = (1/2)^(x / 30)
ln(2/15) = x/30 ln(1/2)
x => 30ln(2/15) / ln(1/2)
I think they want you to "estimate" the value based on your graph and then compare it to the actual answer found mathematically.
Anonymous
a) Use a graphing calculator or any free online graphing program, or a sheet of graphing paper for various values of x, say 5, 10, 15 minutes
b) 28degree is the Temperature, Temperature is given by T(x), so plug in 20 for T(x),
28=60(0.5)^(x/30) + 20
Now, solve for x. (bring x on one side, everything else on the other side)
c) check the number found in part (b) i.e x, the elapsed time, with the graph on part (a)
Does this make sense? Let me know. Good luck!