Exponential Functions: Reading Word Problems

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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 constant percentage over equal time intervals.

Tags

CCSS.HSF-IF.C.8B

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.

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What is a real-world example of exponential growth?

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

Tags

CCSS.HSF-LE.A.1A

Front

What is a real-world example of exponential decay?

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A real-world example of exponential decay is radioactive decay, where the quantity of a radioactive substance decreases over time.

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x, noting that the graph will rise steeply for growth or approach zero for decay.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals 'a'.

Tags

CCSS.HSF-IF.C.7E