Cooling the silly coffee !!!!! emmidiate help Due in a few Hours

**Cooling the silly coffee !!!!! emmidiate help Due in a few Hours**

test y=ax^n and y=Ae^kx

1). i need to investigate a power model in the form y=ax^n by plotting my raw data and log x vs log y

2). i need to investigate a exponential modle in the form y=Ae^kx by plotting the raw data and x vs log y

i now need to use graphs and correlation coefficients to determine the equation of the model that fits your Data.?????

how do i find the equation... my text book only gose briefly and i missed the class due sports, i asked my teachers and friends but they only confused me more.

thank you for the fast help

Re: Cooling the silly coffee !!!!! emmidiate help Due in a few Hours

What **is** your "raw data"? Presummably, each data point is (x, y). Find the two logarithms, and plot point (log(x), log(y)). Do those points seem to be close to a staright line?

The point is that if y= ax^n then lpg(y)= log(ax^n)= nlog(x)+ log(a) where log(y) is a linear function of log(x).

Similarly, if y= ae^(kx) the log(y)= kx+ log(a) where log(y) is a linear function of x.

Re: Cooling the silly coffee !!!!! emmidiate help Due in a few Hours

Hi thanks for being fast,

yes the raw data is in x and y x being time and y the difference in temperature as apart of a table we were given.

what i don't under stand is how do i find A and n in the fist and A and k in the next??

Re: Cooling the silly coffee !!!!! emmidiate help Due in a few Hours

and every time i graph with my graphics cal it doesn't pass the x axis

Re: Cooling the silly coffee !!!!! emmidiate help Due in a few Hours

Is there any reason why "not passing the x-axis" is a problem? If you are referring to finding the x-intercept, you can extend the line until it does cross.

As I said before, the whole point is to try to get, in the first case, log(y)= A log(x)+ B, and, in the second case, log(y)= Ax+ B.

"A", in each case, is the slope of the line: choose two points, (log(x1), log(y1) and (log(x2), log(y2)), to find the slope $\displaystyle \frac{log(y2)- log(y1)}{log(x2)- log(x1)}$ and (x1, log(y1)), (x2, log(y2)) to find the slope $\displaystyle \frac{log(y2)- log(y1)}{x2- x1}$. You can find "B" by using that A with one point: B= log(y)- Alog(x) or B= log(y)- Ax.

Re: Cooling the silly coffee !!!!! emmidiate help Due in a few Hours