Transcendental Numbers and Exponential Functions

This video tutorial covers exponential and logarithmic functions, focusing on their properties, graphing techniques, and applications. It introduces the natural number e, explains how to use calculators for exponential calculations, and discusses the domain and range of these functions. The tutorial also explores financial applications, such as compounded and continuous interest, providing practical examples and calculations.

What is the approximate value of the natural base e?

• 1.61803

• 2.71828

• 1.41421

• 3.14159

Which of the following is a transcendental number?

• 5

• e

• 3

• 2

How is an exponential function generally written?

• f(x) = a/x

• f(x) = x^a

• f(x) = ax + b

• f(x) = a^x

In an exponential function f(x) = a^x, what must be true about the base a?

• a must be greater than 1

• a must be positive and not equal to 1

• a must be zero

• a must be negative

What happens to the graph of f(x) = a^x as x increases, given that a > 1?

• It oscillates

• It decreases

• It increases

• It remains constant

What is the y-intercept of the graph of f(x) = a^x?

• 1

• a

• 0

• a^0

What is the domain of the natural exponential function f(x) = e^x?

• x < 0

• All real numbers

• x > 0

• x >= 0

What is the range of the natural exponential function f(x) = e^x?

• y > 0

• 0 < y < 1

• x > 0

• All real numbers

Which formula is used for calculating compounded interest?

• A = P(1 + r/n)^(nt)

• A = P(1 + rt)

• A = P(1 - r/n)^(nt)

• A = P(1 + r)^t

In the formula for continuous compounding, A = Pe^(rt), what does 'r' represent?

• Rate of interest

• Number of times compounded

• Principal amount

• Time in years