6. Exponential & Logarithmic Functions

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have \$12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

Graph each function. Give the domain and range. ƒ(x) = (1/3)^-x+1

Graph y= 2^x and x = 2^y in the same rectangular coordinate system.

Graph each function. Give the domain and range. ƒ(x) = (1/3)^x+2 - 1

Solve each equation. 4^x-2 = 2^3x+3

Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

Concept Check. If ƒ(x) = a^x and ƒ(3) = 27, determine each function value. ƒ(-1)

The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^-x, r(x) = -4^-x+3

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

The graph of an exponential function is given. Select the function for each graph from the following options:

$f(x) = 3^x, \quad g(x) = 3^{x-1}, \quad h(x) = 3^x - 1, \\f(x) = -3^x, \quad G(x) = 3^{-x}, \quad H(x) = -3^{-x}.$

Begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^x – 1

Begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2.2^x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn g(x) = e^x-1