Exponentials 24-25

Front

What is an exponential function?

Back

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

Front

What does it mean for an exponential function to grow?

Back

An exponential function grows when the base 'b' is greater than 1, resulting in rapid increases in value as 'x' increases.

Front

What does it mean for an exponential function to decay?

Back

An exponential function decays when the base 'b' is between 0 and 1, leading to a rapid decrease in value as 'x' increases.

Front

How do you solve an exponential equation with the same base?

Back

To solve an exponential equation with the same base, set the exponents equal to each other and solve for the variable.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function y = ab^x, which determines the rate of growth or decay.

Front

How do you convert an exponential equation to logarithmic form?

Back

An exponential equation a^b = c can be converted to logarithmic form as log_a(c) = b.

Front

What is the exponential growth formula?

Back

The exponential growth formula is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the exponential decay formula?

Back

The exponential decay formula is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

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

Back

The y-intercept of an exponential function y = ab^x is found by evaluating the function at x = 0, which gives y = a.

Front

What is the significance of the point (0, a) in an exponential function?

Back

The point (0, a) represents the y-intercept of the exponential function, indicating the initial value when x = 0.