The Basics Examples

Find f(9) if f(x) = 3(2.13)^x.

Take the value of 9 and put it in place of x.

f(x) = 3(2.13)^x
f(9) = 3(2.13)⁹
f(9) ≈ 2707

g(x) = 9(0.99)^0.9x. Is this exponential growth or decay?

Remember that y = ab^x is the general form of an exponential equation and what determines growth or decay is the b value. Since the b value is 0.99 which is less than 1, our example is exponential decay.

How many zombies would there be after 3 days if our zombie virus equation from earlier was used? Here it is again:

f(t) = 2.1(4.9)^t

where t is time in days and f(t) is the number of zombies that are "alive."

Take the value of 3 and put it in place of t.

f(t) = 2.1(4.9)^t
f(3) = 2.1(4.9)³
f(3) ≈ 247

The virus hasn't taken over the world yet after 3 days. There are only 247 "decayed" bodies exponentially multiplying themselves.

Build an exponential function from this table of values:

Notice that f(x) changes by a product of . Each value is multiplied by  to get to the next value. This tells us it is an exponential decay function.

f(0) = 0.5. Our initial value is 0.5. We are multiplying by 0.5 every time which is our base. Here is our exponential equation:

f(x) = 0.5(0.5)^x

Determine the exponential function that has an initial value of 2 that increases 9% each year.

Remember that y = ab^x is the general form of an exponential equation. Our initial value, 2, is our a value. An increase of 9% each year, would mean our b value is (1 + 0.09) each year.

f(t) = 2(1.09)^t

Well, by-golly gee-willickers. That was easy.