6. Exponential & Logarithmic Functions

Graph each function. See Example 2. ƒ(x) = 3^x

In Exercises 25-34, 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

Graph each function. See Example 2. ƒ(x) = (1/10)^-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

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 h(x) = e^-x

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = 3^-x

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

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. Find the accumulated value of an investment of $10,000 for 5 years at an interest rateof 1.32% if the money isa. compounded semiannually;b. compounded quarterly;c. compounded monthly;d. compounded continuously.

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

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. Find the accumulated value of an investment of $10,000 for 5 years at an interest rateof 1.32% if the money isa. compounded semiannually;b. compounded quarterly;c. compounded monthly;d. compounded continuously.

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

Solve each equation. See Examples 4–6. (5/2)^x = 4/25

Solve each equation. See Examples 4–6. x^5/2 = 32

Solve each equation. See Examples 4–6. (1/e)^-x = (1/e^2)^(x+1)