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Chapter 4: Problem 3
Write each equation in its equivalent exponential form. $$2=\log _{3} x$$
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Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$2^{x+1}=8$$
Find the domain of each logarithmic function. $$f(x)=\log \left(\frac{x+1}{x-5}\right)$$
Describe a difference between exponential growth and logistic growth.
Students in a mathematics class took a final examination. They took equivalent forms of the exam in monthly intervals thereafter. The average score, \(f(t),\) for the group after \(t\) months was modeled by the human memory function \(f(t)=75-10 \log (t+1), \quad\) where \(\quad 0 \leq t \leq 12 . \quad\) Use \(\quad\) a graphing utility to graph the function. Then determine how many months elapsed before the average score fell below 65.
Hurricanes are one of nature's most destructive forces. These low-pressure areas often have diameters of over 500 miles. The function \(f(x)=0.48 \ln (x+1)+27\) models the barometric air pressure, \(f(x),\) in inches of mercury, at a distance of \(x\) miles from the eye of a hurricane. Graph the function in a \([0,500,50]\) by \([27,30,1]\) viewing rectangle. What does the shape of the graph indicate about barometric air pressure as the distance from the eye increases?
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