Question

What does a represent in y=ax^b?

Answer 1

do you mean
\[y = a b^x\]

Answer 2

My book is showing it as \[y=ax^b\] and is a power law

Answer 3

coefficient ?

Answer 4

ok just clarifying, "b" usually refers to something else

in this case, "a" is the leading coefficient to the polynomial and affects the shape of the graph as in how steep or wide it appears

Answer 5

Ill try to explain some more, I have a set of data that when graphed equates to \[y=1.5184x ^{-0.999}\]
I was told to graph the inverse of one of the variables, and the equation came to
\[y=0.6579x+.0007\]

It then goes on to ask what the slope of the second equation represents in relation to the first equation.

Answer 6

Taking the inverse of the slope gives me the a coefficient of the first equation, but i have no idea what thats telling me.

Answer 7

This is a physics based problem relating mass and acceleration, but I figured it was better to discuss the math here.

Answer 8

is the 2nd equation supposed to be the inverse of 1st equation?

Answer 9

It only asked to invert one variable. Which, in this case, was the y-axis.

Answer 10

ok so you are not taking the inverse function. You are taking reciprocal of each "y" point in your data set, then fitting a new equation to fit the new data?

Answer 11

It seems the answer is that the slope of 2nd function is just the reciprocal of the slope in 1st function

Answer 12

\[ y=1.5184x ^{-0.999} \]
to solve for x, first divide both sides by 1.5184
\[ x^{-0.999}= \frac{y}{1.5184} \]
now "raise each side the the -1/0.999 power""
\[ \left( x^{-0.999}\right)^\frac{-1}{0.999} = \left(\frac{y}{1.5184}\right)^\frac{-1}{0.999} \]

using \( (x^a)^b = x^{ab} \) we get
\[ x=\left(\frac{y}{1.5184}\right)^{-\frac{1000}{999}}= \left(\frac{1.5184}{y}\right)^{\frac{1000}{999}}\]