Question

Urgent!!!

set whether each of the following equations represents a growth or decay


1. f(x)= 3
`^(x)`


2.f(x) = (0.25)
`x^(x)`


3.f(x)=
`(2)/(3x^(x) )`


4.f(x) =
`(3)/(2) x^(x)`

Answer 1

Notice that the written functions are mostly incorrectly written, after a short online search i've found the correct ones, which are the ones i will write in this answer.

A general exponential equation can be written as:

f(x) = A*(r)^x

Where A is the initial value, r is the rate of growth, and x is our variable.

If r > 1, the function represents a growth.

if 0 < r < 1, the function represents a decay.

1) f(x) = 3^x

Here we have r = 3

This is clearly larger than 1, then this function represents a growth.

2) f(x) = (0.25)^x

Here we have r = 0.25, which is smaller than 1 and larger than zero, then this function represents a decay.

3) f(x) = (2/3)^x

here we have r = 2/3 = 0.66

This is larger than zero and smaller than 1, then this function represents a decay.

4) f(x) = (3/2)^x

Here we have r = 3/2 = 1.5

This is larger than 1, then this function represents a growth,