Thread: Convertion/translation of two equations

I have two tasks that I'm unable to work out, and I hope someone could help me :)


TASK 1:
There are three unknown exponential functions:
y1 = f1 (t);
y2 = f2 (t);
y3 = f3 (t):


By measuring the values of t and yi, you get a linear relation between:


Yi = logci (yi) (log to the base of ci)
and t:
Yi = logsi (yi) = Ait + Bi (log to the base of si)




Describe the function f1 in the following way:
y1 = f1 (t) = Ce^(lambda*t)


The values are
i 1 2 3
Ai -1.25 1.53 -1.95
Bi 1.19 1.1 1.95
si 3.76 0.32 0.3


(i is always the base of A, B, s, Y and y)




TASK 2
Translate the equation
ln (y) = a ln (x) + b


to


y = f (x) = cx^r


when a=1.5486 b=0.9309

I'm a little confused about si and ci in Task 1. If , then you take to both sides to get where .

It looks like Task 2 is a similar idea with instead of :


, and setting as before,

The identity follows from the power rule for logarithms.

- Hollywood

Thanks for the assistance! I managed to work it out by plotting in the values and using some of what you wrote

Cheers!