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Q:
Question 5
The population of a rural county is decreasing. The population in 2014 was 230,000 and the population in
2021 was 212,000 . Assuming that decay is exponential (with natural base \( e \) ), what is the yearly decay
rate? State answer as a percentage rounded to one decimal place.
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Q:
La ecuación cartesiana \( \left(x^{2}+y^{2}\right)^{2}=2\left(x^{2}-\right. \)
\( \left.y^{2}\right) \) en coordenadas polares
corresponde a:
\( \begin{array}{l}r^{2}=2 \cos 2 \theta \\ r=6 \cos 2 \theta \\ r^{2}=6 \cos 2 \theta \\ \end{array} \)
Q:
The functions \( f \) and \( g \) are defined as follows.
\[ f(x)=\frac{x}{x^{2}+49} \]
\( g(x)=\frac{x-9}{x^{2}-81} \)
For each function, find the domain.
Write each answer as an interval or union of intervals.
Q:
Complete this assessment to review what you've learned. It will not count toward your grade.
Using the Quotient Rule of Logarithms, the Product Rule of Logarithms, and the Power Rule of Logarithms, how can \( \ln \left(\frac{1}{3 x^{2}}\right) \) be
fully expanded? (1 point)
\( \begin{array}{l}-\ln 3-2 \ln x \\ 0 \ln 1-\ln 3-2 \ln x \\ 0-\ln 3-\ln x \\ -\ln 3-\ln x^{2}\end{array} \)
Q:
\( \log _{7} 10 \approx 1.183 \) and \( \log _{7} 20 \approx 1.540 \), what is \( \log _{7}(10 \cdot 20) \) ? Use the Product Rule of Logarithms to solve. (1 po.
0.357
2.723
1.822
1.302
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Q:
Ethan purchases a car for \( \$ 25,000 \), and the value depreciates by half every 3 years. The time \( t \), in years, that it takes for the value of
a car to reach an amount \( P \), in dollars, is calculated by the logarithmic equation \( t=3 \log _{2}\left(\frac{25,000}{P}\right) \). Which of the following is the
best estimate for the value of the car after 5 years? (1 point)
\( \$ 8,000 \)
\( \$ 10,000 \)
\( \$ 5,000 \)
\( \$ 6,000 \)
Q:
Un medicamento en el
cuerpo humano disminuye a
una tasa de 20\% cada hora.
Si se toma una dosis de 200
mg, ¿Cuánto medicamento
quedará después de 3
horas?
\( 102,4 \mathrm{mg} \)
80 mg
64 mg
120 mg
Q:
Compare the two logarithms by placing \( <_{1}> \), or \( = \) in the response box. (1 point)
\( \frac{\log 200}{\log 8} \square \frac{\ln 200}{\ln 8} \)
Q:
Sketch the graph of each function.
\( y=\frac{1}{2} \cdot\left(\frac{1}{5}\right)^{x-2}-2 \)
Q:
(c) \( \log _{3} \log _{4} \log _{5}(x-5)>0 \)
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