Concept explainers
Suppose that an initial population of 10,000 bacteria grows exponentially at a rate of
(a) Find an initial-value problem whose solution is
(b) Find a formula for
(c) How long does it take for the initial population of bacteria to double?
(d) How long does it take for the population of bacteria to reach 45,000?
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Calculus: Early Transcendentals, Enhanced Etext
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus Enhanced with Graphing Utilities
Calculus: Single And Multivariable
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- In the exponential growth or decay function y=y0ekt, what does y0 represent? What does k represent?arrow_forwardCesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?arrow_forwardThe table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,