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Chapter 4: Problem 88
Evaluate or simplify each expression without using a calculator. $$\ln e$$
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How can you tell whether an exponential model describes exponential growth or exponential decay?
Use the formula \(t=\frac{\ln 2}{k}\) that gives the time for a population with a growth rate \(k\) to double to solve Exercises \(35-36 .\) Express each answer to the nearest whole year. The growth model \(A=4.3 e^{0.01 t}\) describes New Zealand's population, \(A,\) in millions, \(t\) years after 2010 . a. What is New Zealand's growth rate? b. How long will it take New Zealand to double its population?
The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) What percentage of 80 -year-olds have some coronary heart disease?
One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.
Make Sense? In Exercises \(73-76\), determine whether each statement makes sense or does not make sense, and explain your reasoning. When I used an exponential function to model Russia's declining population, the growth rate \(k\) was negative.
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