Exam 4: Exponential and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of $y = \log _ { b } x$ passes through the point $( 1,0 )$ and the line ـــــــــــــــ is a (horizontal/vertical) asymptote.

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\log _ { 9 } 20,412 - \log _ { 9 } 7 - \log _ { 9 } 4$

Solve the equation. - $\log _ { 5 } ( - x ) + \log _ { 5 } ( x - 10 ) = \log _ { 5 } 24$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function $f ( x ) = e ^ { x }$ is the exponential function base and is also called the exponential function.

Determine if the statement is true or false. - $\log _ { 5 } \left( \frac { 1 } { x } \right) = \frac { 1 } { \log _ { 5 } x }$

Write the domain in interval notation. - $f ( x ) = \log _ { 3 } \left( x ^ { 2 } - 9 \right)$

Solve the equation. - $\log _ { 2 } \sqrt { x + 3 } + \log _ { 2 } \sqrt { x } = 1$

The function defined by $f ( x ) = x ^ { 2 } - 9$ is/is not) a one-to-one function, whereas $g ( x ) = x ^ { 2 } - 9 ; x \geq 0$ 0 (is/is not) a one-to-one function.

Choose the one alternative that best completes the statement or answers the question. Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. - $\log _ { 1 / 2 } ( a b c )$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 5 } \left[ \frac { 125 a ^ { 5 } \sqrt { 8 - b } } { c ( b + 7 ) ^ { 2 } } \right]$

Let f be a one-to-one function and let g be the inverse of f. Then $( f \circ g ) ( x ) =$ ________and $\left( g \circ f ^ { \prime } \right) ( x ) =$ ________ .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A function defined by $y = \frac { c } { 1 + a e ^ { - b t } }$ is called aــــــــــــ growth model and imposes a limiting value on $y$ .

Solve the problem. -Bethany needs to borrow $8,000. She can borrow money at 6.9% simple interest for 3 yr or she can borrow at 6.5% with interest compounded continuously for 3 yr. Which option results in less total Interest?

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $5 ^ { 2 z + 3 } = 625$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given positive real numbers $x$ and $b$ such that $b \neq 1 , y = \log _ { b } x$ is the ـــــــــــــ function base $b$ and is equivalent to $b ^ { y } = x$ .

ng, in -From $1995 - 2005$ , the hourly pay for lifeguards at an outdoor swimming pool increased by $2 \%$ per year. The hourly pay, $P ( t )$ , in dollars, $t$ yr after 1995 is given by $P ( t ) = 5.60 ( 1.02 ) ^ { t }$ . What was the hourly pay for the lifeguards in 2,001 ?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The power property of logarithms indicates that for any real number p, $\log _ { b } x ^ { p } =$ for positive real numbers b, x, and y where $b \neq 1$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 8 a \right) - \log ( a + 8 ) \right]$

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = \log _ { 4 } ( x - 1 )$

Solve the problem. -A $\$ 45,000$ inheritance is invested for 15 yr compounded quarterly and grows to $\$ 109,940$ . Find the interest rate. Round to the nearest percent