Exponential growth and decay Warm Up

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.

Front

What does the base of an exponential function indicate?

Back

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

Front

What is the formula for exponential growth?

Back

The formula for exponential growth 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 formula for exponential decay?

Back

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

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, indicating that the value of the function increases rapidly.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the value of the function decreases rapidly.

Front

What does the initial value in an exponential function represent?

Back

The initial value in an exponential function represents the starting amount before any growth or decay occurs.

Front

If a function is modeled by A = 1200(0.85)^x, what type of function is it?

Back

This function represents exponential decay because the base (0.85) is less than 1.

Front

What does a growth rate of 14% per week mean in an exponential function?

Back

A growth rate of 14% per week means that the function increases by 14% of its current value each week.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster increases over time.