Exam 3: Exponential, Logistic, and Logarithmic Functions

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. - $f ( x ) = \log \left( x ^ { 3 } \right)$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = x ^ { 4 }$

State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. - $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 5 \mathrm { x } }$

Find the logistic function that satisfies the given conditions. -

Find the logistic function that satisfies the given conditions. -Initial value $= 12$ , limit to growth $= 36$ , passing through $( 1,24 )$

Solve the problem. -Suppose you contribute to a fund that earns 11.9% annual interest. What should your monthly payment be if you want to accumulate $340,000 in 17 years?

Graph the function. - $f ( x ) = \frac { 9 } { 1 + 2 \cdot 0.6 ^ { x } }$

Find the following using a calculator. Round to four decimal places. - $\log 23$

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\ln x ^ { 5 } y ^ { 5 }$

Solve the problem. -The formula R = log (a/T) + B is used to find the severity (magnitude) of an earthquake based on the amplitude, a, of the associated seismic wave. If one earthquake has a severity of 1.7 on the Richter scale and a second Earthquake has a severity of 5.7 on the Richter scale, how many times more severe (to the nearest whole Number) is the second earthquake than the first?

Solve the problem. -The Richter scale magnitude $\mathrm { R }$ of an earthquake is based on the features of the associated seismic wave and is measured by $\mathrm { R } = \log ( \mathrm { a } / \mathrm { T } ) + \mathrm { B }$ , where a is the amplitude in $\mu \mathrm { m }$ (micrometers), $\mathrm { T }$ is the period in seconds, and B accounts for the weakening of the seismic wave due to the distance from the epicenter. Compute the earthquake magnitude $\mathrm { R }$ when $\mathrm { a } = 210 , \mathrm {~T} = 5$ , and $\mathrm { B } = 3.5$ . (Round to the nearest ten-thousandth.)

Graph the function. Describe its position relative to the graph of the indicated basic function. - $f(x)=2^{x}+1 \text {; relative to } f(x)=2^{x}$

Choose the graph which matches the function. - $f ( x ) = 2 ^ { x + 3 }$

Solve the problem. -The decay of $367 \mathrm { mg }$ of an isotope is given by $\mathrm { A } ( \mathrm { t } ) = 367 \mathrm { e } ^ { - 0.03 \mathrm { t } }$ , where $\mathrm { t }$ is time in years. Find the amount left after 57 years.

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = 3 \cdot 0.2 ^ { x }$

Solve the equation. - $\log _ { 6 } x + \log _ { 6 } ( x - 3 ) = 2$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = 8 ^ { x }$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = - ln (x + 1)

Provide an appropriate response. - $\text { Explain why the range of the exponential function } y = 2 ^ { x } \text { does not include zero. }$

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\log _ { 11 } \left( \frac { \sqrt [ 7 ] { \sqrt { 3 } } } { q ^ { 2 } p } \right)$