Algebra I Regents Review Task #4 (exponential functions)

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 'a' represent in the equation y = a(b^x)?

Back

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

Front

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

Back

The base 'b' indicates the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

How do you determine if a function is exhibiting exponential growth?

Back

A function exhibits exponential growth if the base 'b' is greater than 1.

Front

How do you determine if a function is exhibiting exponential decay?

Back

A function exhibits exponential decay if the base 'b' is between 0 and 1.

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(1 - r)^t, where 'r' is the decay rate and 't' is time.

Front

If a culture of bacteria starts with 5000 cells and dies by 30% each year, what is the decay factor?

Back

The decay factor is 0.7, representing the remaining 70% of the population after each year.

Front

Write the equation for a population that starts at 5000 and decreases by 30% each year.

Back

y = 5000(0.7^x) where x is the number of years.

Front

What is the initial amount in the equation y = 5000(0.7^x)?

Back

The initial amount is 5000.

Front

In the equation y = 0.5(2^x), what type of growth does it represent?

Back

It represents exponential growth.