Sandi,
Have you been studying linear regression?
Penny
Sandi wrote back
Hi Penny I'm a Distant Ed student and I just got this module. It is entitled NonLinear Functions. The first question asked me to write a exponential function. The second question asked me what the difference is between exponential growth and decay and this is the third question(very well could be leading up to linear regression). I understand that an exponential equation is written in the form of y=ab^x. Graphing calculators aren't my friend (still trying to figure out how to use one properly, windows really mess me up, but I think I did scatter plot right) Originally I was going to do the following y=ab^t/p (y being the future amount, a being the initial amount(500), b being type of growth(2 cause it says splitting in two), p being period of growth(24hours) and t being time?not sure what to put or if this should be the24hours. For the time I was going to turn the days into hours so I'd have 24,48,72,96,120,144,168,192,216,240. So y=500(20^? not sure what I'm doing at this point. Is anything I'm doing making sense or should this question be handled a totally different way cause the t and p part have me stumped and second guessing everything.
Any help would be greatly appreciated. Some of the other questions I have are similar to this one so I'm hoping I can use this as a model.
Sandi,
My first thought was much like yours. My thought was to use the equation
y = a b^{kx},
with b = 2 or b = 10 or if you know about natural logarithms, b = e. Now take the logarithm of both sides and the equation becomes
log(y) = log(a b^{kx}) = log(a) + k log(b) x.
If you now let Y = log(y), A = log(a) and m = k log(b) then you can see this is a linear equation
Y = A + m x.
This is a standard technique when you expect the relationship is exponential. Take the logarithm of each value in the ycolumn, in your case the population column, to get Yvalues and construct a scatter plot of Y against x (time in your problem). If the original relationship is exponential this scatter plot will look linear. Use some technique (linear regression) to fit a linear equation Y = A + m x and then, depending on the value of b you picked, recover the values of a and k.
This looks too complex for what seems to be expected of you in this problem so I went back and looked at your data, in particular the population values. What I noticed is that
600 = 500 × 6/5
720 = 600 × 6/5 = 500 × (6/5)^{2}
864 = 720 × 6/5 = 500 × (6/5)^{3
}and so on.
Can you complete the problem now?
Penny
