Exponential Functions

* Exponential Function- A function with a formula of the form f(x)=ab x where a≠0,b>0, and b≠1 * Exponential Growth Function- An exponential function with b>1, and a>0. * Exponential Growth Curve- Graph of exponential growth function * Exponential Decay Function- An exponential function with a>0 and 0<b<1 * Exponential Decay Curve- Graph of exponential decay function * Strictly Increasing- As x-values increase, y-values increase * Strictly Decreasing- As x-values increase, y-values decrease * Asymptote- A line that the graph of a function y=f(x) approaches as the variable x approaches a fixed value or increases or decreases without bound

* In form f(x)=A(b) x * Variable must be in exponent * Domain is set of all real numbers * Graph contains the point (0,a) * Graph does NOT intersect the x-axis * X-axis is horizontal asymptote

* With Function f(x)=A(b) x * If A is positive, then range is y>0 * If A is negative, then range is y<0

* The function is strictly increasing, because as x-values increase, corresponding y-values increase * As x gets larger, f(x) increases without bound * As x gets smaller, f(x) decreases but is always positive and it approaches 0

* Function is strictly decreasing, because as x values increase, corresponding y values decrease * As x gets smaller, f(x) increases without bound * As x gets larger, f(x) decreases but is always positive and it approaches 0

* The graph of the exponential function flips over the x-axis.

* Function in form a x =b * Graph on your calculator * Y 1 =a x * Y 2 =b * Press 2 nd then CALC (TRACE) * Select option 5:intersect * Select both lines, press enter again * X= is the answer * Round answer three decimal places

* P(n)=I(%) y * I=Initial population given in the problem * %= Percent population increases per year +1 * i.e if population increase is 2.5%, then %=1.025 * Y= Years after the initial year * i.e. if initial year is 1993, then 2002=9 * Can be used for interest rates as well

* P(n)=I(%) y * I= Initial population * %= Percent that’s left after each year * i.e if 85% of population is left then %=0.85 * Y= Years after initial year

* Worksheet 2-4