Exam 3: Exponential, Logistic, and Logarithmic Functions

Solve the problem. -How long will it take for $1100 to grow to $4800 at an interest rate of 10.9% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Solve the problem. -Estimate the $y$ -value associated with $x = 15$ as predicted by the natural logarithmic regression equation for the following data.

State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. - $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { - x }$

Match the function with its graph. - $f ( x ) = \log x ^ { 4 }$

Provide an appropriate response. - $\text { Explain why the domain of the logarithmic function } y = \log _ { 2 } x \text { does not include negative numbers. }$

Find the following using a calculator. Round to four decimal places. - $\log 93,900$

Match the function f with its graph. - $f ( x ) = \log _ { 4 } ( x + 1 )$

Solve the problem. -Matthew obtains a 30-year $84,000 house loan with an APR of 7.23%. What is his monthly payment?

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = \ln ( 8 - x ) - 7 ; \quad g ( x ) = \ln x$

Provide an appropriate response. - $f(x)=a^{X}$ The graph of an exponential function with base a is given. Sketch the graph of $g ( x ) = - a x$ . Give the domain and $r$ : of $g$ .

Graph the function. - $f ( x ) = \frac { 3 } { 1 + 4 e ^ { - x } }$

Solve the problem. -The table shows the population of a certain city in various years. The data can be modeled by an exponential function of the form $f ( x ) = b a ^ { x }$ . Use exponential regression to predict the population of the city in the year 2000 . (You will first need to determine the exponential function $\mathrm { f }$ that models this data).

State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. - $f ( x ) = 3 ^ { - x }$

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. - $f ( x ) = 99 \cdot 0.03 ^ { x }$

Solve the problem. -The table shows the number of sales of scooters $y$ , in thousands, $x$ months after they are introduced on the market. Use regression to find a logistic function $\mathrm { f }$ that models this data. Round the constants to the nearest hundredth.

Find the exact solution to the equation. - $\log _ { 5 } x = 2$

Match the function with its graph. - $f ( x ) = \log x ( x - 2 )$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. -f(x) = log3(6x)

Match the function f with its graph. - $f(x)=\log _{1 / 4}(x+4)$

Solve the problem. -By how many orders of magnitude do a $20 bill and a nickel differ?