Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term.

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is found by evaluating f(0), which equals a.

Front

What is the formula for the product of exponential expressions?

Back

The product of exponential expressions with the same base can be simplified using the formula: a^m * a^n = a^(m+n).

Front

What is the formula for the quotient of exponential expressions?

Back

The quotient of exponential expressions with the same base can be simplified using the formula: a^m / a^n = a^(m-n).

Front

What is the value of b in the exponential function f(x) = 3 * b^x if f(1) = 9?

Back

To find b, set up the equation: 3 * b^1 = 9. Solving gives b = 3.

Front

What is the exponential growth formula?

Back

The exponential growth formula is given by f(t) = a * e^(kt), where a is the initial amount, k is the growth rate, and t is time.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the growth rate is positive (k > 0), while exponential decay occurs when the growth rate is negative (k < 0).

Front

How do you simplify (2x^3)(4x^2)?

Back

To simplify, multiply the coefficients and add the exponents: (2*4)x^(3+2) = 8x^5.

Front

What is the common ratio for the sequence: 3, 15, 75...?

Back

The common ratio is 5.