Exponential: Growth and Decay

Front

What is an exponential function?

Back

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

Front

What does the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function is the value of 'y' when 'x' is 0. It represents the initial value of the function.

Tags

CCSS.HSF-IF.C.7E

Front

How do you find the y-intercept of the function y = 1.25(5^x)?

Back

To find the y-intercept, substitute x = 0 into the function: y = 1.25(5^0) = 1.25.

Tags

CCSS.HSF-IF.C.7E

Front

What is the rate of growth in the function y = 5(1.27^x)?

Back

The rate of growth is the percentage increase represented by the base of the exponent. In this case, it is 27%.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating the future value of an investment with exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the rate of interest, and t is the time in years.

Front

What does the rate of decay in an exponential function indicate?

Back

The rate of decay indicates the percentage decrease in value over a specific time period, represented by the base of the exponent in a decay function.

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the rate of decay in the function y = 35(0.65^x)?

Back

The rate of decay is calculated as (1 - base) * 100%. Here, it is (1 - 0.65) * 100% = 35%.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(b^x), where 0 < b < 1.

Front

How can you determine if a function represents exponential growth or decay?

Back

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

Tags

CCSS.HSF-IF.C.8B