If the national economy shrank at an annual rate of 6% per year for 3 consecutive years, then the economy shrank by 18% over the three year period. the economy shrank by what per6 over the three year period?

Using an exponential function, it is found that the economy shrank by 16.94% over the three year period.

--------------------------------

The equation for a decaying exponential amount is given by:

In which:

--------------------------------

--------------------------------

0.1694*100% = 16.94%.

The economy shrank by 16.94% over the three year period.

A similar problem is given at link

You want to find x such that

... 1 - x = (1 - 6%)³

... x = 1 - (0.94)³ = 1 - 0.830584 = 0.169416

... x ≈ 16.9%

The economy shrank by about 16.9% over the three-year period.

c

step-by-step explanation:

c

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!