Questions from General Calculus


Q: An isotope of sodium, 24Na, has a half-life

An isotope of sodium, 24Na, has a half-life of 15 hours. A sample of this isotope has mass 2 g. (a). Find the amount remaining after 60 hours. (b). Find the amount remaining after t hours. (c). Estima...

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Q: Use a graphing calculator with exponential regression capability to model the population

Use a graphing calculator with exponential regression capability to model the population of the world with the data from 1950 to 2000 in Table 1 on page 56. Use the model to estimate the population in...

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Q: Investigate the possible shapes for epicycloids. Use methods similar to Problems

Investigate the possible shapes for epicycloids. Use methods similar to Problems 2–4.

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Q: Use the graphs of x = f (t) and y

Use the graphs of x = f (t) and y = g (t) to sketch the parametric curve x = f (t), y = g (t). Indicate with arrows the direction in which the curve is traced as increases.

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Q: The table gives the population of the United States, in millions

The table gives the population of the United States, in millions, for the years 1900–2000. Use a graphing calculator with exponential regression capability to model the US population...

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Q: If you graph the function f (x) = 1 -

If you graph the function f (x) = 1 - e1/x /1 + e1/x you’ll see that f appears to be an odd function. Prove it.

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Q: Use the Law of Exponents to rewrite and simplify the expression.

Use the Law of Exponents to rewrite and simplify the expression.

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Q: (a). Write an equation that defines the exponential function with

(a). Write an equation that defines the exponential function with base a > 0. (b). What is the domain of this function? (c). If a ≠ 1, what is the range of this function? (d). Sketch the general shape...

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Q: (a). How is the number e defined? (

(a). How is the number e defined? (b). What is an approximate value for e? (c). What is the natural exponential function?

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Q: (a). What is a one-to-one function

(a). What is a one-to-one function? (b). How can you tell from the graph of a function whether it is one-to-one?

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