Chapter 1: Problem 60
Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places. $$\log _{3} 30$$
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A culture of bacteria has a population of 150 cells when it is first observed. The population doubles every 12 hr, which means its population is governed by the function \(p(t)=150 \cdot 2^{t / 12},\) where \(t\) is the number of hours after the first observation. a. Verify that \(p(0)=150,\) as claimed. b. Show that the population doubles every \(12 \mathrm{hr}\), as claimed. c. What is the population 4 days after the first observation? d. How long does it take the population to triple in size? e. How long does it take the population to reach \(10,000 ?\)
A cylindrical tank with a cross-sectional area of \(100 \mathrm{cm}^{2}\) is filled to a depth of \(100 \mathrm{cm}\) with water. At \(t=0,\) a drain in the bottom of the tank with an area of \(10 \mathrm{cm}^{2}\) is opened, allowing water to flow out of the tank. The depth of water in the tank at time \(t \geq 0\) is \(d(t)=(10-2.2 t)^{2}\). a. Check that \(d(0)=100,\) as specified. b. At what time is the tank empty? c. What is an appropriate domain for \(d ?\)
Large intersection point Use any means to approximate the intersection point(s) of the graphs of \(f(x)=e^{x}\) and \(g(x)=x^{123}\).
The population \(P\) of a small town grows according to the function \(P(t)=100 e^{t / 50},\) where \(t\) measures the number of years after \(2010 .\) How long does it take the population to double?
Right-triangle relationships Use a right triangle to simplify the given expressions. Assume \(x>0.\) $$\cos \left(\tan ^{-1}\left(\frac{x}{\sqrt{9-x^{2}}}\right)\right)$$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
