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Chapter 3: Problem 7
Approximate each number using a calculator. Round your answer to three decimal places. $$e^{2.3}$$
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The formula \(S=C(1+r)^{t}\) models inflation, where \(C=\) the value today, \(r=\)the annual inflation rate, and \(S=\)the inflated value t years from now. Use this formula to solve. Round answers to the nearest dollar. If the inflation rate is \(3 \%,\) how much will a house now worth \(\$ 510,000\) be worth in 5 years?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that exponential functions and logarithmic functions exhibit inverse, or opposite, behavior in many ways. For example, a vertical translation shifts an exponential function's horizontal asymptote and a horizontal translation shifts a logarithmic function's vertical asymptote.
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. Use this function to solve Exercises \(133-134\) 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?
Will help you prepare for the material covered in the next section. $$\text { Solve: }(x-3)^{2} > 0$$
Graph \(f(x)=2^{x}\) and its inverse function in the same rectangular coordinate system.
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