Exponential Functions Section 1.2

Concavity A function is concave up if it bends upward as we move from left to right. A function is concave down if it bends down as we move from left to right. “Palm” method

P(t) = P0at P(t) is the amount at time t P0 is the amount when t = 0 a is the growth factor per time unit a > 1 => exponential growth a < 1 => exponential decay (a - 1)=> percent of change

Terms Half-life is the time it takes in exponential decay for the quantity to be reduced by a factor of one-half Doubling time is the time it takes in exponential growth for the quantity to double is size

P(t) = P0ekt A special case of exponential equations. Used for continuous growth or decay k is the percent of change K>0 continuous growth K<0 continuous decay Note ek = a

Assignment Page 15-17 1-39 odds plus Hand in problems 14 and 30