Chapter 3: Problem 25
How many times brighter is a star with apparent magnitude 2 than a star with apparent magnitude \(17 ?\)
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Chapter 3: Problem 25
How many times brighter is a star with apparent magnitude 2 than a star with apparent magnitude \(17 ?\)
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Suppose a colony of bacteria starts with 200 cells and triples in size every four hours. (a) Find a function that models the population growth of this colony of bacteria. (b) Approximately how many cells will be in the colony after six hours?
Find all numbers \(x\) that satisfy the given equation. $$ (\log (6 x)) \log x=5 $$
Explain why every function \(f\) with exponential growth can be represented by a formula of the form \(f(x)=c \cdot 2^{k x}\) for appropriate choices of c and \(k\).
Suppose your cell phone rings at a noise of 74 decibels and you normally speak at 61 decibels. (a) What is the ratio of the sound intensity of your cell phone ring to the sound intensity of your normal speech? (b) How many times louder does your cell phone ring seem than your normal speech?
Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{4}\left(u^{3} v^{4}\right) $$
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