Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it.
ADDED: An exponential decay trace's flat-looking region has its own special name: an "asymptote".
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A curve
Exponential functions increase for all values of x, Logistic growth patterns appear to increase exponentially however they eventually platou out on a maximum y value
If the exponent has the variable of time in it, then it will be either exponential growth (such as compound interest for example), or exponential decay (such as radioactive materials, or a capacitor discharging). If the time constant (coefficient of the time variable) is positive then it is growth, if the time constant is negative, then it is decay.
implementation of exponential groth
They are similar because the population increases over time in both cases, and also because you are using a mathematical model for a real-world process. They are different because exponential growth can get dramatically big and bigger after a fairly short time. Linear growth keeps going up the same amount each time. Exponential growth goes up by more each time, depending on what the amount (population) is at that time. Linear growth can start off bigger than exponential growth, but exponential growth will always win out.