Notice the way the function in Figure is decreasing. Each hour a smaller quantity of the drug is removed than in the previous hour. This is because as time passes, there is less of the drug in the body to be removed. Compare this to the exponential growth in Figure , where each step upward is larger than the previous one. Notice, however, that both graphs are concave up. The General Exponential Function Provided > 0, the largest possible domain for the exponential function is all real numbers. The a reason we do not want 0 is that, for example, we cannot define if < 0. Also, we do not a a1/2 a ≤ usually have = 1, = = is then a constant function. a P P01t P0 The value of is closely related to the percent growth (or decay) rate. For example, if = 1.03, then a a is growing at 3%; if = 0.94, then is decaying at 6%. P a P
Notice the way the function in Figure is decreasing. Each hour a smaller quantity of the drug is removed than in the previous hour. This is because as time passes, there is less of the drug in the body to be removed. Compare this to the exponential growth in Figure , where each step upward is larger than the previous one. Notice, however, that both graphs are concave up. The General Exponential Function Provided a > 0, the largest possible domain for the exponential function is all real numbers. The reason we do not want a ≤ 0 is that, for example, we cannot define a1/2 if a < 0. Also, we do not usually have a = 1, P = P01t = P0 is then a constant function. The value of a is closely related to the percent growth (or decay) rate. For example, if a = 1.03, then P is growing at 3%; if a = 0.94, then P is decaying at 6%.
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