Learning Materials
Features
Discover
Chapter 3: Problem 90
Use the One-to-One Property to solve the equation for \(x\). $$\ln (x-7)=\ln 7$$
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
The sales \(S\) (in thousands of units) of a new CD burner after it has been on the market for \(t\) years are modeled by \(S(t)=100\left(1-e^{k t}\right) .\) Fifteen thousand units of the new product were sold the first year. (a) Complete the model by solving for \(k\). (b) Sketch the graph of the model. (c) Use the model to estimate the number of units sold after 5 years.
A laptop computer that costs $$\$ 1150$$ new has a book value of $$\$ 550$$ after 2 years. (a) Find the linear model \(V=m t+b\). (b) Find the exponential model \(V=a e^{k t}\) (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the computer after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.
Find the exponential model \(y=a e^{b x}\) that fits the points shown in the graph or table. $$ \begin{array}{|l|l|l|} \hline x & 0 & 4 \\ \hline y & 5 & 1 \\ \hline \end{array} $$
The populations \(P\) (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by \(P=\frac{2632}{1+0.083 e^{0.0500 t}}\) where \(t\) represents the year, with \(t=0\) corresponding to \(2000 .\) (Source: U.S. Census Bureau) (a) Use the model to find the populations of Pittsburgh in the years \(2000,2005,\) and 2007 . (b) Use a graphing utility to graph the function. (c) Use the graph to determine the year in which the population will reach 2.2 million. (d) Confirm your answer to part (c) algebraically.
The yield \(V\) (in millions of cubic feet per acre) for a forest at age \(t\) years is given by \(V=6.7 e^{-48.1 / t}\) (a) Use a graphing utility to graph the function. (b) Determine the horizontal asymptote of the function. Interpret its meaning in the context of the problem. (c) Find the time necessary to obtain a yield of 1.3 million cubic feet.
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