Question

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

Answer 1

y = (5.2)^x is exponential growth.
The exponential equation is y = a * b^x
If b > 1 then the function is exponential growth.
If 0 < b < 1 then the function is exponential decay.

Answer 2

An exponential function is given by:

`y = ab^x` ......[1]

where,

a is the initial amount.

If b > 1, then this is exponentially growth function.

If 0<b<1, then this is exponentially decay function.

As per the statement:

Given the function:

`y = (5.2)^x`

On comparing with equation [1] we have;

a = 1 and b = 5.2

Since, b = 5.2 > 1

⇒the given function is exponentially growth function.

therefore, the function
`y = (5.2)^x` represents exponentially growth function.