Questions from General Calculus

Q: If a bacteria population starts with 100 bacteria and doubles every three

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after hours is n – f (t) = 100 ∙ 2t/3. (a). Find the inverse of this function and explain...

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.

Q: When a camera flash goes off, the batteries immediately begin to

When a camera flash goes off, the batteries immediately begin to recharge the flash’s capacitor, which stores electric charge given by Q (t) = Q0 (1 – e-t/a). (The maximum charge capacity is Q0 and is...

Q: Find the exponential function f (x) = Cax whose graph

Find the exponential function f (x) = Cax whose graph is given.

Q: If f (x) = 5x, show that f (

If f (x) = 5x, show that f (x + h) - f (x)/h = 5x (5h – 1)/h

Q: Suppose you are offered a job that lasts one month. Which

Suppose you are offered a job that lasts one month. Which of the following methods of payment do you prefer? I. One million dollars at the end of the month. II. One cent on the first day of the month,...

Q: Suppose the graphs of f (x) = x2 and g

Suppose the graphs of f (x) = x2 and g (x) = 2x are drawn on a coordinate grid where the unit of measurement is 1 inch. Show that, at a distance 2 ft to the right of the origin, the height of the grap...

Q: Compare the functions f (x) = x10 and g (

Compare the functions f (x) = x10 and g (x) = ex by graphing both f and g in several viewing rectangles. When does the graph of g finally surpass the graph of f?

Q: Use a graph to estimate the values of such that ex >

Use a graph to estimate the values of such that ex > 1,000,000,000.

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

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