HOW TO KNOW IF A FUNCTION IS EXPONENTIAL OR NOT

Next to each function, write "yes" if it is an exponential function. If the answer is "no", write an explanation why not.

Problem 1 :

y = -6(3)^x

Solution:

y = -6(3)^x

This function exactly in the form a(b)^x.

So, it is an exponential function.

Problem 2 :

y = 3(5/2)^-x

Solution:

y = 3(5/2)^-x

This function exactly in the form a(b)^x.

So, it is an exponential function.

Problem 3 :

y = 7x^-3

Solution:

y = 7x^-3

y = a(b)^x

For the above function the base is the variable x, and the exponent is the constant -3. So, it is not an exponential function.

Problem 4 :

y = 3(-4)^x

Solution:

y = 3(-4)^x

y = a(b)^x

The base b, must be a positive number other then 1.

So, it is not an exponential function.

Problem 5 :

y = 92x¹⁰³

Solution:

y = 92x¹⁰³

y = a(b)^x

For the above function the base is the variable x, and the exponent is the constant 103. So, it is not an exponential function.

Problem 6 :

y = 14(-8)^x

Solution:

y = 14(-8)^x

y = a(b)^x

The base b, must be a positive number other then 1.

So, it is not an exponential function.

Problem 7 :

y = -5(12)^2x

Solution:

y = -5(12)^2x

Solution:

y = -5(12)^2x

This function exactly in the form a(b)^x.

So, it is an exponential function.

Problem 8 :

y = 13(32)^-2x

Solution:

y = 13(32)^-2x

This function exactly in the form a(b)^x.

So, it is an exponential function.