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 an exponential function?

Back

The common ratio in an exponential function is the base 'b' raised to the power of 'x', which determines how much the function grows or decays.

Front

What is the value of b^0?

Back

b^0 = 1 for any non-zero base 'b'.

Front

How do you classify an exponential function as growth or decay?

Back

An exponential function is classified as growth if the base 'b' is greater than 1 (b > 1) and as decay if the base 'b' is between 0 and 1 (0 < b < 1).

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

If A = 1200(0.85)^6, is this exponential growth or decay?

Back

This is exponential decay because the base (0.85) is less than 1.

Front

If A = 10(1.01)^3, is this exponential growth or decay?

Back

This is exponential growth because the base (1.01) is greater than 1.

Front

How do you write an exponential function for a situation?

Back

To write an exponential function, identify the initial value and the growth or decay rate, then use the formula y = a(1 ± r)^x.

Front

What does the term 'initial value' mean in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the function.