Learning Materials
Features
Discover
Chapter 3: Problem 71
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{5} 13$$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Students in a mathematics class took a final examination. They took equivalent forms of the exam in monthly intervals thereafter. The average score, \(f(t),\) for the group after \(t\) months was modeled by the human memory function \(f(t)=75-10 \log (t+1), \quad\) where \(\quad 0 \leq t \leq 12 . \quad\) Use \(\quad\) a graphing utility to graph the function. Then determine how many months elapsed before the average score fell below 65.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that exponential functions and logarithmic functions exhibit inverse, or opposite, behavior in many ways. For example, a vertical translation shifts an exponential function's horizontal asymptote and a horizontal translation shifts a logarithmic function's vertical asymptote.
Use a calculator with an \(\left[e^{x}\right]\) key to solve. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through 2013. (BAR GRAPH CAN'T COPY) The data can be modeled by $$ f(x)=x+31 \text { and } g(x)=32.7 e^{0.0217 x} $$ in which \(f(x)\) and \(g(x)\) represent the percentage of high school seniors who applied to more than three colleges \(x\) years after 1980\. Use these functions to solve . Where necessary, round answers to the nearest percent. In college, we study large volumes of information \(-\) information that, unfortunately, we do not often retain for very long. The function $$ f(x)=80 e^{-0.5 x}+20 $$ describes the percentage of information, \(f(x),\) that a particular person remembers \(x\) weeks after learning the information. a. Substitute 0 for \(x\) and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for \(x\) and find the percentage of information that is remembered after 1 week. c. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after one year (52 weeks).
Nigeria has a growth rate of 0.025 or \(2.5 \% .\) Describe what this means.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine