7.1 Exponential Growth p. 478 What you should learn: Goal 1

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Presentation transcript:

7.1 Exponential Growth p. 478 What you should learn: Goal 1 Graph and use Exponential Growth functions. Write an Exponential Growth model that describes the situation. Goal 2 A2.5.2 7.1 Graph Exponential Growth Functions

Exponential Function f(x) = bx where the base b is a positive number other than one. Graph f(x) = 2x 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 2 raised to any power Will NEVER be zero!! y = 0

Lets look at the activity on p. 479 This shows of y = a * 2x 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)

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

Example 1 Graph 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

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

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 bx-h + k Sketch y = a bx h = ??? k = ??? Move your 2 points h units left or right … and k units up or down Then sketch the graph with the 2 new points.

Example 3 Graph y = 3·2x-1 - 4 Lightly sketch y = 3·2x Passes thru (0,3) & (1,6) h= 1, k= -4 Move your 2 points to the right 1 and down 4 AND your asymptote k units (4 units down in this case)

D= all reals R= all reals >-4 y = -4

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

A=P(1+r/n)nt Compound Interest 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) quarterly c) daily A=1000(1+ .08/1)1x1 = 1000(1.08)1 ≈ $1080 A=1000(1+.08/4)4x1 =1000(1.02)4 ≈ $1082.43 A=1000(1+.08/365)365x1 ≈1000(1.000219)365 ≈ $1083.28

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