Writing Exponential Functions from Word Problems

Front

What does the base in an exponential function represent?

Back

The base represents the growth or decay factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.

Front

How do you identify exponential growth from an equation?

Back

Exponential growth is identified when the base of the exponential function is greater than 1.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

What does the 'a' value in an exponential function represent?

Back

The 'a' value represents the initial amount or the y-intercept of the function.

Front

If a population triples every hour, how is this represented in an exponential function?

Back

It is represented as f(h) = a(3)^h, where 'a' is the initial population.

Front

What is the difference between growth and decay in exponential functions?

Back

Growth occurs when the base is greater than 1, while decay occurs when the base is between 0 and 1.

Front

How do you convert a percentage growth rate to a growth factor?

Back

To convert a percentage growth rate to a growth factor, add 1 to the percentage expressed as a decimal. For example, a 6% growth rate becomes 1 + 0.06 = 1.06.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a(1 - r)^t, where 'r' is the decay rate.

Front

How do you write an exponential function for an investment that grows at a certain percentage?

Back

The function is written as B(t) = P(1 + r)^t, where P is the principal amount, r is the growth rate, and t is time.

Front

What does a scale factor of 0.85 indicate in an exponential function?

Back

A scale factor of 0.85 indicates a decay of 15%.