Is this exponential growth or decay? y= -5(1/3)^-x

[Aroused Guy]

y= -5(1/3)^-x

Ok, here is what I am thinking. Since there is a negative exponent, it reverses what the base should be. Therefor, I am thinking the function represents exponential GROWTH. However, I am not sure about this negative five. When I graph points relating to the function, as x-increases, y-decreases. This is where I am confused. Doesn't this mean exponential DECAY if y-decreases and x-increases? But, I was instructed to only look at the base and exponent. By the way, here's a very rough sketch of what the function looks like: http://img232.imageshack.us/my.php?image=54193368.png

Please help me! Thank you.

 

[Deleted member 4993]

Re: Is this exponential growth or decay?

y= -5(1/3)^-x

Ok, here is what I am thinking. Since there is a negative exponent, it reverses what the base should be. Therefor, I am thinking the function represents exponential GROWTH. However, I am not sure about this negative five. When I graph points relating to the function, as x-increases, y-decreases. This is where I am confused. Doesn't this mean exponential DECAY if y-decreases and x-increases? But, I was instructed to only look at the base and exponent. By the way, here's a very rough sketch of what the function looks like: http://img232.imageshack.us/my.php?image=54193368.png

Please help me! Thank you.

As x increases (moving from left to right) - y decreases (goes down) - hence decay.

 

[wjm11]

Re: Is this exponential growth or decay?

y= -5(1/3)^-x
here's a very rough sketch of what the function looks like: http://img232.imageshack.us/my.php?image=54193368.png

Just an "FYI": I know it's a rough sketch, but it seems to show that the y-axis is an asymptote. It is not. The y-intercept is -5.

 

[fasteddie65]

Re: Is this exponential growth or decay?

y= -5(1/3)^-x
here's a very rough sketch of what the function looks like: http://img232.imageshack.us/my.php?image=54193368.png

Another way to think of this: y = -5(1/3)^-x = -5(3)^x, which is clearly growth, since the base 3 > 0. However, the coefficient of -5 flips the entire graph upside down, so it seems to indicate decay. You really have to examine the function carefully.

And, BTW, the horizontal asymptote is the x-axis.