Examine the following and determine whether it shows exponential growth or
decay. *
f (x) = 1, 800(0.45)
Growth
Decay

It shows exponential decay and not growth

Step-by-step explanation:

In this question, we are asked to examine the mathematical relation and determine if it shows growth or decay

The mathematical relation in the question shows decay.

Why?

This is because looking at the mathematical equation that represents the model of the equation, we can see that the multiplying term present alongside the original term is a number that is less than 1. As this number is less than 1, subsequent multiplications will surely be less than 1 also. This means each subsequent term will have a value which is less than the preceding term. This makes a case for why the model is for decay and not for growth.

Had it been that the term we have in the bracket is a number which is greater than 1, even let’s say 1.0001, this will ensure that subsequent terms will be higher than preceding term and as such we can explicitly state that what we have is growth and not decay. But unfortunately, this is not the case here

8y^50

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!