University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2013
Views:

177

Pages:

1
Author:

wystlwr8mf

Exponential Functions, Models, and Operations with Logarithms Determine whether the model is exponential growth or decay: (f(x)=-2(3)^{x}) decay (f(x)=2^{x}+2) growth (f(x)=2(\frac{1}{2})^{x}) decay (f(x)=3(2)^{x}) growth (f(x)=5(1.7)^{x}) growth (f(x)=2(.23)^{x}) decay Describe the shifts that occur from f(x) to g(x): (f(x)=2(\frac{1}{2})^{x}) left 1 (f(x)=3(2)^{x}) up 3 (f(x)=5(1.7)^{x}) right 1, up 4 (f(x)=2(.23)^{x}) down 2 Write the logarithm equation in exponential form: (log_{4}64=3) (4^{3}=64) (log_{3}81=4) (3^{4}=81) (log_{7}(\frac{1}{49})=-2) (7^{-2}=\frac{1}{49}) (log_{4}81=4) (4^{4}=81) Write the exponential equation in logarithmic form: (5^{3}=125) (log_{5}125=3) (8^{4}=4096) (log_{8}4096=4) (3^{\frac{1}{4}}=81) (log_{3}81=\frac{1}{4}) (10^{1}=10) (log_{10}10=1) Evaluate the logarithm using the change of base formula: (log_{2}16) (log_{10}16/log_{10}2=4) (log_{9}1000) (log_{10}1000/log_{10}9=3.107) (log_{\frac{1}{7}}1) (log_{10}1/log_{10}(1/7)=0) (log_{10}3) (log_{10}3=0.477) Use the properties of logarithms to condense the expression into a single logarithm or expand into many: (log_{5}x+log_{5}y-log_{5}z) (log_{5}\frac{xy}{z}) (log_{8}B-log_{8}t) (log_{8}\frac{B}{t}) (\frac{1}{3}log_{5}x+2log_{5}y^{2}) (log_{5}\sqrt[3]{x}y^{4}) (2log_{x}x-3log_{y}y^{3}-log_{z}z^{4}) (log_{x}x^{2}-log_{y}y^{9}-log_{z}z^{4}) (\frac{1}{2}log_{x}x-3log_{y}y+5log_{z}z) (log_{x}\sqrt{x}-log_{y}y^{3}+log_{z}z^{5}) (2ln(x^{3})+3ln(y^{3})-4ln(z)) (ln\frac{x^{6}y^{9}}{z^{4}}) (log_{5}5x) (log_{5}5+log_{5}x=1+log_{5}x) (log_{2}\frac{y}{2}) (log_{2}y-log_{2}2=log_{2}y-1) (log_{3}xyz) (log_{3}x+log_{3}y+log_{3}z) (log_{4}\frac{x\sqrt{y}}{z}) (log_{4}x+\frac{1}{2}log_{4}y-log_{4}z) (log_{2}(x^{5}z^{3}\sqrt{y})) (5log_{2}x+3log_{2}z+\frac{1}{2}log_{2}y) (log_{2}\frac{x^{4}y^{5}}{z^{3}}) (4log_{2}x+5log_{2}y-3log_{2}z)