How do I identify an exponential growth/decay function on a graph? I'm assuming that if the curve moves from left to right, upwards, it is growth, and if it moves left to right, downwards, then it is decay. Please tell me whether this reasoning is right or wrong.
basically correct
Though that may not guarantee that the curve is exponential. Given that assumption, your reasoning is correct.
yes, you are correct
example of exponential growth graph
http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex
example of exponential decay graph
http://www.wolframalpha.com/input/?i=plot+y+%3D+%281%2F2%29%5Ex
Thanks!
Your reasoning is partially correct. To determine whether a function represents exponential growth or decay, you need to consider the direction and shape of the graph.
For exponential growth, the function will have a positive base raised to a power (typically written as y = a * b^x, where a is the initial value and b is the growth factor). In this case, the graph will start at a non-zero positive value and will increase rapidly as x increases. As you mentioned, the graph will move from left to right and upwards.
Similarly, for exponential decay, the function will have a positive base raised to a negative power (typically written as y = a * b^-x). The initial value (a) will also be positive. In this case, the graph will start at a positive value and decrease rapidly as x increases. So, you are correct in noting that the graph will move from left to right and downwards.
However, it's important to note that the orientation of the graph alone (i.e., moving from left to right and upwards or downwards) is not enough to determine whether it represents exponential growth or decay. You also need to consider the shape, steepness, and the symmetry of the graph.
In summary, to identify an exponential growth function, the graph will move from left to right and upwards, and for an exponential decay function, the graph will move from left to right and downwards. But the key is not just the orientation of the graph; you should also consider the shape and characteristics of the graph.