Exponential Functions Test Review

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

How do you model exponential decay?

Back

Exponential decay can be modeled using the function f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

Convert the expression √(7x) to rational exponent form.

Back

(7x)^(1/2)

Front

What is the value of 160,000 after 20 years with a 5% annual increase?

Back

$424,527.63

Front

Write (3x)³ in radical form.

Back

∜(3x)³ = (3x)^(3/4)

Front

What does the term 'decay rate' refer to in exponential functions?

Back

The decay rate is the percentage by which a quantity decreases over a specific period of time.

Front

How do you simplify the expression 2^4?

Back

2^4 = 16.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

If a population of bacteria decreases by 14.9% per minute, what is the decay factor?

Back

The decay factor is 1 - 0.149 = 0.851.