Chapter 10: Problem 24
In Exercises, use a graphing utility to graph the function. $$ y=4^{x}+3 $$
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 10: Problem 24
In Exercises, use a graphing utility to graph the function. $$ y=4^{x}+3 $$
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeIn Exercises, find the derivative of the function. $$ f(x)=x \ln e^{x^{2}} $$
The term \(t\) (in years) of a \(\$ 200,000\) home mortgage at \(7.5 \%\) interest can be approximated by \(t=-13.375 \ln \frac{x-1250}{x}, x>1250\) where \(x\) is the monthly payment in dollars. (a) Use a graphing utility to graph the model. (b) Use the model to approximate the term of a home mortgage for which the monthly payment is \(\$ 1398.43 .\) What is the total amount paid? (c) Use the model to approximate the term of a home mortgage for which the monthly payment is \(\$ 1611.19 .\) What is the total amount paid? (d) Find the instantaneous rate of change of \(t\) with respect to \(x\) when \(x=\$ 1398.43\) and \(x=\$ 1611.19\). (e) Write a short paragraph describing the benefit of the higher monthly payment.
In Exercises, use a calculator to evaluate the logarithm. Round to three decimal places. $$ \log _{5} 12 $$
The effective yield is the annual rate \(i\) that will produce the same interest per year as the nominal rate \(r\). (a) For a rate \(r\) that is compounded continuously, show that the effective yield is \(i=e^{r}-1\). (b) Find the effective yield for a nominal rate of \(6 \%\), compounded continuously.
In Exercises, graph and analyze the function. Include any relative extrema and points of inflection in your analysis. Use a graphing utility to verify your results. $$ y=\frac{x}{\ln x} $$
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