It is predicted that for the next eight years the number of connected devices in households across the world will be 18.36% more than the previous year. what type of relationship most appropriately models of situation? exponential growth exponential decay linear decrease linear increase

This situation would be modeled by an exponential growth representation. This is because we are increasing by 18.36 percent each year. This means that for each year, we take the number of households from last year and grow it by 18.36 percent. Thus, throughout the years, you accumulate more and more households, which leads to even bigger numbers.

If we were adding, for example, 18 households each year, the situation would be a linear increase situation. This is because the increase stays constant and does not change based on the numbers of the last iteration. Additionally, we know that our relationship is not a decreasing one because the problem says "more than the previous year," showing that there is growth occurring.

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!