Warm Up for Unit 3 Test

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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value (b > 1). Exponential decay occurs when a quantity decreases at a rate proportional to its current value (0 < b < 1).

Front

What is the general form of an exponential decay function?

Back

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

Front

What is the decay rate in the function y = 1500(1 - 0.015)^t?

Back

The decay rate is 0.015, or 1.5% per year.

Front

How do you determine the amount left after a certain time in an exponential decay scenario?

Back

Use the formula y = a(1 - r)^t, substituting 'a' for the initial amount, 'r' for the decay rate, and 't' for time.

Front

What is the equation of a function that models exponential growth?

Back

An example is y = a(b^x) where b > 1, indicating that the quantity increases over time.

Front

What is the value of y when x = 2 in the function y = 32(1/4)^x?

Back

y = 32(1/4)^2 = 32(1/16) = 2.

Front

What does the base of an exponential function represent?

Back

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

Front

What is the initial value in the function y = 512(1/4)^x?

Back

The initial value is 512, which is the value of y when x = 0.

Front

How can you identify an exponential decay function from a graph?

Back

An exponential decay function will show a decreasing curve that approaches the x-axis but never touches it.