Exam 5: Inverse, Exponential, and Logarithmic Functions

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm{f}^{-1}(2)$

Solve the equation. - $36 ^ { x } = 6$

In the formula N $\mathrm { N } = \mathrm { Ie } ^ { kt } , \mathrm { N }$ N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 72 million cars in a certain Country, decreasing by 3.4% annually. How many years will it take for this country to have 47 million cars? Round to the nearest year.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $f ( x ) = 5 ^ { - x }$

Round to the nearest thousandth. - $2 ^ { x } = 23$

The population growth of an animal species is described by $F ( t ) = 400 \log ( 2 t + 3 )$ where t is measured in months. Find the population of this species in an area 6 months after the species is introduced.

Solve the equation and express the solution in exact form. - $\ln x - \ln ( x - 3 ) = \ln 7$

Which of the following is the same as $3 \log ( 4 x )$ for $x > 0$ ?

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 5 ; [ - 3,3 ] \text { by } [ - 40,40 ]$

Why does logaa always equal 1 for any valid base a?

Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by $f ( x ) = 35.8 e ^ { 0.17 x }$ Approximate how many years it takes for the number of hamburgers served to reach 54 million. Round to the nearest year.

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $\{ ( 6 , - 7 ) , ( 11 , - 6 ) , ( 9 , - 5 ) , ( 7 , - 4 ) \}$

Given $f ( x ) = 8 ^ { x }$ , evaluate the following. (a) $f \left( \log _ { 8 } 6 \right)$ (b) $f \left[ \log _ { 8 } ( 3 \ln 8 ) \right]$ (c) $\mathrm { f } \left[ \log _ { 8 } ( \ln 8 ) \right]$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 5 ^ { x }$ . Find $f ( - 2 )$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $\log _ { 6 } 13 - \log _ { 6 } x$

Suppose f(x) $f ( x ) = 28.9 + 1.5 \log ( x + 1 )$ odels salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity (to the Nearest hundredth) when the depth is 572 meters.

Round to the nearest thousandth. - $7^{3 x} = 8 ( x + 1 )$

A certain noise has an intensity I of $9.61 \times 10 ^ { - 5 }$ . Given that decibel level D is related to intensity by $\mathrm { D } = 10 \log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$ , where $\mathrm { I } _ { 0 }$ is $10 ^ { - 12 }$ , determine the decibel level of the noise. Round your answer to the nearest decibel.

Determine whether the statement is true or false. -Any polynomial function of odd degree is a one-to-one function.

Determine whether or not the function is one-to-one. -