Answered: Solve for the exact value of x. log,…

Name: this is a practice problem, not a graded assignment Log Equations (1st
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: this is a practice problem, not a graded assignment Log Equations (1st Degree)Apr 08, 11:09:21 PMWatch help videoSolve for the exact value of x.log, (5æ) + 4 log, (2) = 3Answer:Submit AnswerPrivacy Policy Terms of ServiceCopyright 2021 DeltaMath.com.

Math

Algebra

Solve for the exact value of x. log, (5æ) + 4 log, (2) = 3 Answer: Submit Answer

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 104RE

See similar textbooks

Similar questions

Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.
The Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, the light is absorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensity I at depth x is given by the Beer-Lambert Law: I=I0ekx where I0 is the light intensity at the surface and k is a constant that depends on the murkiness of the water see page 402. A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. Light intensity decreases exponentially with depth. Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the murkiness constant k for this lake? Hint: If your calculator gives you a function of the form I=abx, convert this to the form you want using the identities bx=eln(bx)=exlnb. See Example 1b. Make a scatter plot of the data, and graph the function that you found in part a on your scatter plot. If the light intensity drops below 0.15 lumen lm, a certain species of algae cant survive because photosynthesis is impossible. Use your model from part a to determine the depth below which there is insufficient light to support this algae. Depth ft Light intensity lm Depth ft Light intensity lm 5 10 15 20 13.0 7.6 4.5 2.7 25 30 35 40 1.8 1.1 0.5 0.3
Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?
Logistic Growth Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: p(t)=d1+kea Where c, d, and k are positive constants. For a certain fish population in a small pond d=1200, k=11, c=0.2, and t is measured in years. The fish were introduced into the pond at time t=0 . How many fish were originally put in the pond? Find the population after 10, 20, and 30 years. Evaluate p(t) for large values of t. What value does the population approach as t? Does the graph shown confirm your calculations?
The Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, thelight isabsorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensityI at depth x is given by the Beer-Lambert Law: I=I0ekx Where I0 the light intensity at the surface and k isis a constant that depends on the murkiness of the water (see page 402). A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. (a) Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the “murkiness” constant kfor this lake?(Hint: if your calculator gives you a function of the form I=abx .convert this to the form you want using the identities bx=eIn(bx)=exInb . See Example 1(b).) (b) Make a scatter plot of the data, and graph the function that you found in part (a) on your scatter plot. (c) If the intensity drops below 0.15 lumen (lm) , a certain species of algae can’t survive because photosynthesis is impossible. Use your model from part (a) to determine the depth below which there is insufficient light to support this algae.
More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?