Thread: Need Help Writing Math Problem As Expression

Hello, I need help with the following math problem. It needs to be written as an expression.

Problem: An experiment is underway to test the effect of extreme temperatures on a newly developed liquid. Two hours into the experiment the temperature of the liquid is measured to be -17 degrees celsius. After eight hours of the experiment, the temp. of the liquid is -47 degrees celsius. Assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so.


Any help with this problem will be greatly appreciated.

Thanks!
David

Hello, David!

An experiment tests the effect of extreme temperatures on a liquid.
Two hours into the experiment, the temperature of the liquid is -17° C.
After eight hours of the experiment, the temp. of the liquid is -47° C.

Assume that the temperature has been changing at a constant rate
throughout the experiment and will continue to do so.

Write an expression for this experiment.

Since the change is constant, we have a linear function: .y .= .ax + b

. . When x = 2, y = -17: . -17 .= .2a + b

. . When x = 8, y = -47: . -47 .= .8a + b


We have a system of equations: . [1] .2a + b .= .-17
. . . . . . . . . . . . . . . . . . . . . . . . [2] .8a + b .= .-47

Subtract [1] from [2]: . 6a = -30 . → . a = -5

Substitute into [1]: . 2(-5) + b .= .-17 . → . b = -7


Therefore, the function is: . y .= .-5x - 7

Originally Posted by David7299

Hello, I need help with the following math problem. It needs to be written as an expression.

Problem: An experiment is underway to test the effect of extreme temperatures on a newly developed liquid. Two hours into the experiment the temperature of the liquid is measured to be -17 degrees celsius. After eight hours of the experiment, the temp. of the liquid is -47 degrees celsius. Assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so....

Hello David,

I'm not quite certain whether I understand this problem right or not.

If the rate of changing is constant then you have to do with an exponential function:

Let T(t) be the temperature at the time t. T_0 is the temperature at the time t = 0.

T(t)=T_0 * e^(k * t)
Be careful not to mix the different tT's.

You know: T(2) = -17°C and T(8) = -47°C. Plug in these values into the equation:

-17=T_0 * e^(k * 2)
-47=T_0 * e^(k * 8)

From the first equation you can calculate T_0 = (-17)/(e^(2k)). Plug in this result into the 2nd equation and you'll get k = (ln(47)-ln(17))/6 ≈ 0.16945.

And T_0 ≈ -12.112°C.

Now you can assemble all these results to an equation:

T(t) = -12.112 * e^(0.16945 * t)

EB

I want to thank both of you so much. It helped me out alot. Thanks for taking the time out and helping. Sincerely, David