Exam 4: Exponential and Logarithmic Functions

Find the value of the expression. -Let $\log _ { \mathrm { b } } \mathrm { A } = 3.455$ and $\log _ { \mathrm { b } } \mathrm { B } = 0.192$ . Find $\log _ { \mathrm { b } } \frac { \mathrm { A } } { \mathrm { B } }$ .

Solve the problem. -The function $D ( h ) = 5 e ^ { - 0.4 h }$ can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present After 11 hours?

Solve the problem. -Suppose that $f ( x ) = 3 ^ { x }$ . If $f ( x ) = \frac { 1 } { 729 }$ , what is $x$ ?

Solve the equation. - $\log _ { 6 } ( x + 3 ) = 3$

Solve the problem. -The amount of a certain drug in the bloodstream is modeled by the function $y = y _ { 0 } e ^ { - 0.40 t }$ , where y0 is the amount of the drug injected (in milligrams) and t is the elapsed time (in hours). Suppose that 10 milligrams are Injected at 10:00 A.M. If a second injection is to be administered when there is 1 milligram of the drug present in The bloodstream, approximately when should the next dose be given? Express your answer to the nearest Quarter hour.

Graph the function. - $f ( x ) = \left( \frac { 3 } { 4 } \right) ^ { x }$ A) B) C) D)

The function f is one-to-one. Find its inverse. - $f ( x ) = ( x + 2 ) ^ { 3 } - 8$

Find the present value. Round to the nearest cent. -To get $2000 after 10 years at 9% compounded semiannually

Solve the problem. - $\mathrm { pH } = - \log _ { 10 } \left[ \mathrm { H } ^ { + } \right]$ Find the $\mathrm { pH }$ if the $\left[ \mathrm { H } ^ { + } \right] = 3.9 \times 10 ^ { - 8 }$ .

Solve the problem. -The bacteria in a container quadruples every day. If there are initially 100 bacteria, write an equation that models the number of bacteria A after d days. How many bacteria will there be after 1 week?

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$

Solve the problem. -The revenue for a dot.com company is projected to double each year for the first 5 years. If the revenue for the first year is $2 million, write a function showing the revenue R after x years. What is the revenue for the fourth year?

Graph the function. - f(x)=5|x| A) B) C) D)

Solve the equation. - $\ln \sqrt { x + 2 } = 4$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\ln e \sqrt { 7 }$

Solve the equation. - $\left( \frac { 7 } { 6 } \right) ^ { x } = \frac { 36 } { 49 }$

Change the exponential expression to an equivalent expression involving a logarithm. - $2.3 ^ { x + 5 } = 15$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)$

Solve the problem. -If Emery has $1,100 to invest at 9% per year compounded monthly, how long will it be before he has $1,400? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)

Find the effective rate of interest. -5.5% compounded quarterly