Writing Exponential Functions

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 in an exponential function represent?

Back

The base in an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Front

Write an exponential function to model a situation where a quantity doubles every year starting from 100.

Back

f(t) = 100(2)^t.

Front

What is the formula for exponential growth?

Back

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

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80.

Front

How do you determine the initial value in an exponential function?

Back

The initial value is represented by 'a' in the function f(x) = a(b)^x, and it is the value of the function when x = 0.

Front

What does the exponent in an exponential function represent?

Back

The exponent represents the number of time periods that have passed, affecting the growth or decay of the quantity.

Front

Write an exponential function for a population of 500 that grows at a rate of 4% per year.

Back

P(t) = 500(1.04)^t.

Front

What is the significance of the number 1 in the growth formula f(t) = a(1 + r)^t?

Back

The number 1 represents the original amount before growth occurs.