# Calc 1.2 - ; if 0 &amp;lt; a &amp;lt; 1 , we have...

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1.2 Exponential Functions Constant growth factor = exponential growth To recognize that a table of t and P values comes from an exponential function = P0at , look for ratios of P values that are constant for equally spaced t values The graph of a function is concave-up if it bends upward as we move lfet to right; it is concave down if it bends downward. We say P is an exponential function of t with base a if = P P0at Where P0 is the initial quantity (when t= 0) and a is the factor by which P changes when t increases by 1. If a > 1, we have exponential growth

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Unformatted text preview: ; if 0 &amp;lt; a &amp;lt; 1 , we have exponential decay. The half-life of an exponentially decaying quantity is the time required for the quantity to be reduced by a factor of one half The doubling time of an exponentially increasing quantity is the time required for the quantity to double. Exponential growth = P P0at or = P P0ekt Exponential decay = Q Q0at or = -Q Q0e kt We say that P and Q are growing or decaying at a continuous rate of k. Quadratic + + ax2 bx c parabola A degree n equation has at most n-1 turns** = ek a lna k...
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## This note was uploaded on 06/26/2008 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.

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Calc 1.2 - ; if 0 &amp;lt; a &amp;lt; 1 , we have...

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