Chapter 3: Problem 69
One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.
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Chapter 3: Problem 69
One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.
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Write each equation in its equivalent exponential form. $$\log _{6} 216=y$$
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 the exponential decay model, \(A=A_{0} e^{k t},\) to solve Exercises \(28-31 .\) Round answers to one decimal place. The half-life of thorium- 229 is 7340 years. How long will it take for a sample of this substance to decay to \(20 \%\) of its original amount?
The formula \(S=C(1+r)^{t}\) models inflation, where \(C=\) the value today, \(r=\)the annual inflation rate, and \(S=\)the inflated value t years from now. Use this formula to solve. Round answers to the nearest dollar. If the inflation rate is \(6 \%,\) how much will a house now worth \(\$ 465,000\) be worth in 10 years?
Exercises \(51-56\) present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data. (If applicable, in Exercise \(76,\) you will use your graphing utility to obtain these functions.) Hamachiphobia $$\begin{array}{lcc}\hline & \begin{array}{c} \text { Percentage } \\ \text { Who Won't } \\ \text { Try Sushi } \end{array} & \begin{array}{c} \text { Percentage Who } \\ \text { Don't Approve of } \\ \text { Marriage Equality } \end{array} \\ \hline \text { Millennials } & 42 & 36 \\ \text { Gen X } & 52 & 49 \\ \text { Boomers } & 60 & 59 \\ \text { Silent/Greatest } & 72 & 66 \\ \text { Generation } & & \end{array}$$
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