Writing Exponential Functions (Word Problems)

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

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

Back

The initial value in an exponential function is represented by 'a' in the equation f(x) = a(b)^x. It indicates the value of the function when x = 0.

Front

What does the base of an exponential function represent?

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

How do you write an exponential function for a situation where a quantity triples every day?

Back

If a quantity starts at 'a' and triples every day, the function can be written as f(x) = a(3)^x.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(b)^x, where 0 < b < 1.

Front

How do you determine the decay rate from an exponential decay function?

Back

The decay rate can be found by subtracting the base from 1. For example, in f(x) = a(0.85)^x, the decay rate is 1 - 0.85 = 0.15 or 15%.

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

How do you convert a word problem into an exponential function?

Back

Identify the initial value, the growth or decay factor, and the time period. Then, use the form f(x) = a(b)^x to write the function.

Front

What does it mean for a quantity to double every 'n' days?

Back

If a quantity doubles every 'n' days, the exponential function can be expressed as f(t) = a(2)^(t/n), where 'a' is the initial amount.

Front

How do you find the number of cells after 'h' hours if they triple every hour?

Back

If the initial number of cells is 'a' and they triple every hour, the function is f(h) = a(3)^h.