Reminder Round all answers to two decimal places unless otherwise indicated.
Using the Laws of Logarithms For Exercises 1 through 6, suppose that
To evaluate:
The given expression.
Answer to Problem 1E
Solution:
The expression
Explanation of Solution
Given:
The values
The expression is
Approach:
Following laws of logarithms are to be referred wherever applicable:
1) Product law:
2) Quotient law:
3) Power law:
Calculation:
Consider the expression.
Substitute
Therefore, the expression
Conclusion:
Hence, the expression
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Chapter 4 Solutions
FUNCTIONS+CHANGE -WEBASSIGN
- Reminder Round all answers to two decimal places unless otherwise indicated. Dispersion Model Animal populations move about and disperse. A number of models for this dispersion have been proposed, and many of them involve the logarithm. For example, in 1965, O.H.Paris released a large number of pill bugs and after 12 hours recorded the number n of individuals that could be found within r meters from the point of release. He reported that the most satisfactory model for this dispersion was n=0.772+0.297logr+6.991r. a.Make a graph of n versus r for the circle around the release point with the radius 15 meters. b.How many pill bugs were to be found within 2 meters from the release point? c.How far from the release point would you expect to find only a single individual?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. An Exponential Model with Unit Adjustment Show that the following data are exponential and find a formula for an exponential model. Note: It will be necessary to make a unit adjustment. For this exercise, round your answers to three decimal places. t g(t) t g(t) 0 38.30 12 16.04 4 28.65 16 11.99 8 21.43 20 8.97arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Logistic Model A population grows according to the logistic model. The r value is 0.02 and the environmental carrying capacity is 2500. Write the logistic equation satisfied by the population if N(0)=100.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. The pH Scale Acidity of a solution is determined by the concentration H of hydrogen ions in the solution measured in moles per liter of solution. Chemists use the negative of the logarithm of the concentration of hydrogen ions to define the pH scale: pH=logH Lower pH values indicate a more acidic solution. a.Normal rain has a pH value of 5.6. Rain in the eastern United States often has a pH level of 3.8. How much more acidic is this than normal rain? b.If the pH of water in lake falls below a value of 5, fish often fail to reproduce. How much more acidic is this than normal water with a pH of 5.6?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Making an Exponential ModelShow that the accompanying data are exponential and find a formula for an exponential model. t f(t) t f(t) 0 3.80 3 4.27 1 3.95 4 4.45 2 4.11 5 4.62arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning