Suppose that P(t) is an exponential function. t 1 3 P(t) 31.2 162.24 843.648 Find the formula for P(t).

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and explain the range and domain for each. function (or the arctan function). Draw the relevant graphs 7. EXPONENTIAL FUNCTIONS AND THEIR DERIVATIES (1) Recall the definition of an exponential function. First, the basics. Let a be a positive real number. Then • for n a positive integer, a" = • for n = 0. a" = for n a negative integer, say n = -k, a" = • for x = a rational number, at 1 9 . for x an irrational number, a" = • = at-y (aª)³ = (ab) = I (5) ● P - = be inaction (2) Properties of exponents: For any real numbers x, y and a, b positive real numbers, • a+y = 00 (3) Let f(x) = b. Here b is called MTH 32 • What happens when b< 0? . What happens when b = 0? What happens with b = 1? Explain in detail. 37 and x is called the 64

8. Find a formula for each graph using the general exponential model. (Note: these graphs are not drawn to scale.) y = f(x)| (-2,100) y (0,4) ·x y = g(x) (1,3) (3,18.75) -X