Why Does y=c*a^x Not Fit Data w/Negative Y & Positive X?

[jimmy123]

i don't understand this...why will y=c*a^x not fit data which has negative y-values and positive x-values?... Will that same data fit y=c*a^x+b?

thanks in advance

 

[atqamar]

Think about this: What is the domain and range of $$y=ca^x$$? As $$x$$ increases or decreases, will the domain and range change? It helps to look at a graph of this exponential function.

 

[HallsofIvy]

i don't understand this...why will y=c*a^x not fit data which has negative y-values and positive x-values?... Will that same data fit y=c*a^x+b?

thanks in advance

??Actually it might. You just have to take c to be negative! Since a^x itself is always positive (whether x is negative or positive, c*a^x will be negative as long as c is negative.

If you want to try to fit to points that have y values both positive and negative, then you will have to try something like c*a^x+ b.

Of course, in the first case, since you have only two parameters, a and c, to determine, you can force it to fit more than two points. y= c*a^x+ b as three parameters, so you can fit that to three points.

 

[atqamar]

Halls makes a good point.
Rather than analyzing the function with positive and negative values of $$c$$ and $$a$$, you can fit any two points with this function since it is in its most general form. Plus, you don't have to assume $$c$$ is restricted to be a positive number.

Try this: Find an exponential function in the form $$y=ca^x$$ by solving for $$c$$ and $$a$$ to fit points $$(-2,-3)$$ and $$(3,2)$$.