Question

Without graphing, determine whether the function y = \((5.2)^x\) represents exponential growth or exponential decay.

How do I do this? I know it has something to do with rate?

If the rate is larger than 1 it grows, if it is less than 1 it decays.

Answer 1

What is the base?

Answer 2

It does not give me a base.

Answer 3

Let's say we have the expression:
\[3^5\]

Answer 4

What is the exponent?

Answer 5

The exponent is 5.

Answer 6

What is the base?

Answer 7

The base is 3.

Answer 8

Let's say we have the expression
\[(5.2)^x\]
What is the base?

Answer 9

The base would be 5.2.

Answer 10

So your problem did give you the base after all.

Answer 11

And is the base greater than one or less than one?

Answer 12

It is greater.

Answer 13

Therefore, it is exponential growth.

Answer 14

Thank you :)