Next Quadratic Relationships Between Quantities: Mastery Test
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1
As a part of the Save Nature campaign, the city forest department has decided to grow more trees. To kick off the campaign, they start by
planting 2 pine trees. It has been decided that every year they will increase the amount of trees by 1 tree less than the square of the previous
year's tree count. Which of the following recursive formulas can be used to determine the total number of trees planted in the future? Assume
there is unlimited space for trees, and n is the number of years of the program's operation.
O A. Inti
OB. Int1
(in) + 1, where f(1) = 2
In - 1)where f(1) = 2
(m) – 1, where f(1) = 2
Un + 1)?, where f(1) = 2
oc. Inti
OD. Inti
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asdfghkl

step-by-step explanation:

asdfghkl

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!

b. 2 and 4

step-by-step explanation:

$113.42

i hope that is right.

step-by-step explanation: