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Chapter 4: Problem 8
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{3 x-1}=125$$
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Use properties of logarithms to condense logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. \(\log x+7 \log y\)
We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years affer 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ Use this function to solve Exercises \(38-42\) How well does the function model the data showing a world population of 6.1 billion for \(2000 ?\)
Students in a psychology class took a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score for the group, \(f(t),\) after \(t\) months was modeled by the function $$f(t)=88-15 \ln (t+1), \quad 0 \leq t \leq 12$$ a. What was the average score on the original exam? b. What was the average score after 2 months? 4 months? 6 months? 8 months? 10 months? one year? c. Sketch the graph of \(f\) (either by hand or with a graphing utility). Describe what the graph indicates in terms of the material retained by the students.
Make Sense? In Exercises \(73-76\), determine whether each statement makes sense or does not make sense, and explain your reasoning. Because carbon-14 decays exponentially, carbon dating can determine the ages of ancient fossils.
Complete the table for a savings account subject to contimuous compounding ( \(A=P e^{n}\) ). Round answers to one decimal place. Amount Invested 17,425 dollar Annual Interest Rate 4.25% Accumulated Amount 25,000 dollar Time \(t\) in Years _______
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