Exam 4: Exponential and Logarithmic Functions

Model Exponential Growth and Decay Solve. -The value of a particular investment follows a pattern of exponential growth. In the year 2000 , you invested money in a money market account. The value of your investment $t$ years after 2000 is given by the exponential growth model $\mathrm { A } = 3800 \mathrm { e } ^ { 0.062 \mathrm { t } }$ . When will the account be worth $\$ 6639$ ?

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \sqrt [ 3 ] { \frac { \mathrm { x } ^ { 5 } \mathrm { y } } { 36 } }$

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 2 } ( x + 1 ) + \log _ { 2 } ( x - 5 ) = 4$

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Suppose that you have $11,000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded continuously or 7.6% compounded semiannually?

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $729 ^ { x } = 81$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $2 ( 3 x - 7 ) = 4$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 7 } \left( \log _ { 7 } x + \log _ { 7 } y \right) - 5 \log _ { 7 } ( x + 3 )$

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \mathrm { C } ^ { - 4 }$

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $\ln 1$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log ( x - 3 )$ .

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $7 ^ { x } = 6 ^ { x + 7 }$

Evaluate the expression without using a calculator. - $\log 10 \frac { 1 } { \sqrt { 10 } }$

Use Compound Interest Formulas Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) \text { and } A = P e ^ { r t } \text { to solve }$ -Find the accumulated value of an investment of $19,000 at 8% compounded annually for 10 years.

Solve the problem. -The population in a particular country is growing at the rate of $1.7 \%$ per year. If $7,638,000$ people lived there in 1999 , how many will there be in the year 2004 ? Use $f ( x ) = y _ { 0 } e ^ { 0.017 t }$ and round to the nearest ten-thousand.

Evaluate the expression without using a calculator. - $\log _ { 8 } \frac { 1 } { 8 }$

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 2 } 13 ^ { - 5 }$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $3 ^ { x + 7 } = 4$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 2 } ( x - 5 ) - \log _ { 2 } ( x - 2 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 19 } \left( \frac { \sqrt [ 3 ] { 10 } } { n ^ { 2 } m } \right)$

Solve the problem. -The rabbit population in a forest area grows at the rate of $4 \%$ monthly. If there are 190 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use $y = 190 ( 2.7 ) ^ { 0.04 t }$