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 a positive real number, and 'x' is the exponent.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the function increases over time (b > 1), while exponential decay occurs when the function decreases over time (0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(1 - r)^x, where 'r' is the decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

If a population doubles every year, what is the growth factor?

Back

The growth factor is 2.

Tags

CCSS.HSF-LE.A.1A

Front

How do you determine if a function is exponential growth or decay from its equation?

Back

If the base 'b' in f(x) = a(b^x) is greater than 1, it is growth; if 'b' is between 0 and 1, it is decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for continuous compound interest?

Back

A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

Front

What does the 'e' represent in the continuous compound interest formula?

Back

The 'e' is Euler's number, approximately equal to 2.71828, and is the base of natural logarithms.

Front

How do you find the growth rate from an exponential function?

Back

The growth rate can be found by rearranging the function to the form f(x) = a(1 + r)^x and solving for 'r'.

Tags

CCSS.HSF-IF.C.8B

Front

What is the value of the function f(x) = 400(1 + 0.03)^x when x = 5?

Back

f(5) = 400(1.03)^5 ≈ 400(1.159274) ≈ 463.71.

Tags

CCSS.HSF-IF.C.8B