8.1 Exponential Growthp. 465

Exponential Functionf(x) = bx where the base b is a positive number other than one.Graph f(x) = 2xNote the end behavior x f(x)x- f(x)0y=0 is an asymptote

AsymptoteA line that a graph approaches as you move away from the originThe graph gets closer and closer to the line y = 0 .But NEVER reaches ity = 02 raised to any powerWill NEVER be zero!!

Lets look at the activity on p. 465This shows of y= a * 2x Passes thru the point (0,a) (the y intercept is a)The x-axis is the asymptote of the graphD is all reals (the Domain)R is y>0 if a>0 and y

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

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

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

Example 2Graph y = - (3/2)xPlot (0, -1) and (1, -3/2)Connect with a curveMark asymptoteD=??All realsR=???All reals < 0y = 0

To graph a general Exponential Function:y = a bx-h + kSketch y = a bxh= ??? k= ??? Move your 2 points h units left or right and k units up or downThen sketch the graph with the 2 new points.

Example 3 Graph y = 32x-1-4Lightly sketch y=32xPasses thru (0,3) & (1,6)h=1, k=-4Move your 2 points to the right 1 and down 4 AND your asymptote k units (4 units down in this case)

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

Nowyou try one!Graph y= 23x-2 +1State the Domain and Range!D= all realsR= all reals >1y=1

Compound InterestA=P(1+r/n)ntP - Initial principal r annual rate expressed as a decimaln compounded n times a yeart number of yearsA amount in account after t years

Compound interest exampleYou 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) dailyA=1000(1+ .08/1)1x1 = 1000(1.08)1 $1080A=1000(1+.08/4)4x1 =1000(1.02)4 $1082.43A=1000(1+.08/365)365x1 1000(1.000219)365 $1083.28