An exponential function is one where the exponent or power is the variable, such as

f(x) = 4^{x}

In this function, we get:

f(0) = 4^{0} = 1

f(1) = 4^{1} = 4

f(2) = 4^{2} = 16

f(3) = 4^{3} = 64

f(-2) = 4^{-2} = 1/4^{2} = 1/16

f(½) = 4^{½} = √4 = 2

f(1½) = 4^{3/2} = (√4)^{3} = 2^{3} = 8

**Example**

Use the following function to find f(1½)

f(x) = 3(16)^{x} - 2

**Answer**

To find f(1½), we substitute 3/2 for x to get:

f(1½) = 3(16)^{3/2} - 2

16^{3/2} is (16^{1/2})^{3} = 4^{3 }= 64 so we get

f(1½) = 3 x 64 - 2 = 192 - 2 = 190

f(1½) = **190**