Precálculo preguntas y respuestas

Mitchell is an ecologist studying bonobos, a species of ape that lives in the Congolian rainforest. When he started his study, there was a population of about 40,000 bonobos. After one year, he estimated that the population had decreased to 39,200 . Based on his data, Mitchell expects the population to continue decreasing each year. Write an exponential equation in the form \( y=a(b)^{x} \) that cal model the bonobo population, \( y, x \) years after Mitchell began studying them. Use whole numbers, decimals, or simplified fractions for the values of a and \( b \). \( y=\square \) To the nearest hundred, what can Mitchell expect the bonobo population to be 7 years after the study began? bonobos

Find the domain of the function. \[ f(x)=\ln \left(9-x^{2}\right) \] Write your answer as an interval or union of intervals.

5) Find the equation of the exponential function that goes through \( \left(-1, \frac{2}{5}\right) \) and \( (2,50) .(4 \) pts)

Below is the graph of \( y=\left(\frac{1}{2}\right)^{x} \). Translate it to become the graph of \( y=\left(\frac{1}{2}\right)^{x+1}-4 \).

Below is the graph of \( y=4^{x} \). Translate it to become the graph of \( y=4^{x-2}-1 \)

Below is the graph of \( y=\left(\frac{1}{3}\right)^{x} \) Translate it to become the graph of \( y=\left(\frac{1}{3}\right)^{x+4}+2 \).

45. Suku ke-3 dibagi suku ke-2 dari \( \frac{2^{-n+1}}{n} \) adalah... \( \begin{array}{ll}\text { A. } 4 & \text { D. } \frac{1}{4} \\ \text { B. } 3 & \text { E. } \frac{1}{48} \\ \text { C. } \frac{1}{3} & \end{array} \)

\( \frac { z ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \)

Consider the function \( f(x)=\sqrt{2-x}+6 \) for the domain \( (-\infty, 2] \). Find \( f^{-1}(x) \), where \( f^{-1} \) is the inverse of \( f \). Also state the domain of \( f^{-1} \) in interval notation.

Consider the function \( f(x)=\sqrt{x-1}+2 \) for the domain \( [1, \infty) \). Find \( f^{-1}(x) \), where \( f^{-1} \) is the inverse of \( f \). Also state the domain of \( f^{-1} \) in interval notation.