8.1 Exponential Growth p. 465. Exponential Function f(x) = b x where the base b is a positive number other than one. Graph f(x) = 2 x Note the end behavior.

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Presentation transcript:

8.1 Exponential Growth p. 465

Exponential Function f(x) = b x where the base b is a positive number other than one. Graph f(x) = 2 x Note the end behavior x→∞ f(x)→∞ x→-∞ f(x)→0 y=0 is an asymptote

Asymptote A line that a graph approaches as you move away from the origin The graph gets closer and closer to the line y = 0 ……. But NEVER reaches it y = 0 2 raised to any power Will NEVER be zero!!

Lets look at the activity on p. 465 This shows of y= a * 2 x Passes thru the point (0,a) (THE Y-INTERCEPT IS “a”) The x-axis is the asymptote of the graph D is all reals (the Domain) R is y>0 if a>0 and y<0 if a<0 (the Range) Compare graphing calculator graphs

These are true of: y = ab x If a>0 & b>1 ……… The function is an Exponential Growth Function

Example 1 Graph y = ½ 3 x Plot (0, ½) and (1, 3/2) Then, from left to right, draw a curve that begins just above the x-axis, passes thru the 2 points, and moves up to the right

y = 0 Always mark asymptote!! D+ D= all reals R= all reals>0

Example 2 Graph y = - (3/2) x Plot (0, -1) and (1, -3/2) Connect with a curve Mark asymptote D=?? All reals R=??? All reals < 0 y = 0

To graph a general Exponential Function: y = a b x-h + k Find your asymptote from k Pick values for x. Try to make your exponent value 0 or 1. Complete your T chart (Find y). Sketch the graph.

Example 3 Graph y = 3·2 x-1 -4 h = 1, k = −4 asymptote y = −4 Pick x values x y 1 2 −1 2 D= all reals R= all reals >-4 y = -4

Now…you try one! Graph y= 2·3 x-2 +1 State the Domain and Range! D= all reals R= all reals >1 y=1

Compound Interest A=P(1+ r / n ) nt P - Initial principal r – annual rate expressed as a decimal n – compounded n times a year t – number of years A – amount in account after t years

Compound interest example You deposit $1000 in an account that pays 8% annual interest. Find the balance after I year if the interest is compounded with the given frequency. a) annually b) quarterlyc) daily A=1000(1+.08/1) 1x1 = 1000(1.08) 1 ≈ $1080 A=1000(1+.08/4) 4x1 =1000(1.02) 4 ≈ $ A=1000(1+.08/365) 365x1 ≈1000( ) 365 ≈ $

Assignment P. 469, odd, 49-51, 68-69