Chapter 4: Problem 53
Use a calculator to evaluate the logarithm. Round your result to three decimal places.\(\ln \sqrt{6}\)
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The yield \(V\) (in millions of cubic feet per acre) for a forest at age \(t\) years is given by \(V=6.7 e^{-48.1 / t}, \quad t>0\) (a) Use a graphing utility to find the time necessary to obtain a yield of \(1.3\) million cubic feet per acre. (b) Use a graphing utility to find the time necessary to obtain a yield of 2 million cubic feet per acre.
Solve the exponential equation algebraically. Approximate the result to three decimal places.\(\left(1+\frac{0.075}{4}\right)^{4 t}=5\)
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(3 \ln 5 x=10\)
Radioactive Decay What percent of a present amount of radioactive cesium \(\left({ }^{137} \mathrm{Cs}\right)\) will remain after 100 years? Use the fact that radioactive cesium has a half-life of 30 years.
Bacteria Growth The number \(N\) of bacteria in a culture is given by the model \(N=250 e^{k t}\), where \(t\) is the time (in hours), with \(t=0\) corresponding to the time when \(N=250\). When \(t=10\), there are 320 bacteria. How long does it take the bacteria population to double in size? To triple in size?
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