Exponential Functions: Reading Word Problems

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. It describes growth or decay processes.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' in an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth in a word problem?

Back

Exponential growth can be identified in a word problem by phrases indicating that a quantity increases by a consistent percentage over equal time intervals.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation 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 difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount over time.

Front

How can you solve a word problem involving exponential decay?

Back

To solve a word problem involving exponential decay, identify the initial amount, the decay rate, and use the formula y = a * (1 - r)^t.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What does 'e' represent in exponential functions?

Back

The constant 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models.

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x, noting that the function approaches the x-axis (asymptote) but never touches it.

Tags

CCSS.HSF-IF.C.7E

Front

What is a real-world example of exponential growth?

Back

A real-world example of exponential growth is population growth, where the population increases by a percentage each year.

Tags

CCSS.HSF-LE.A.1A