Hi need early giving out 98 points
you : )

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

2)f(x)=10(2)^x

3)Graph attached

4) Amber will have 192 and 3145728 shares on day 3rd and 10th respectively

Ben will have 54 and 118,098 shares on day 3rd and 10th respectively

Carter will have 80 and 10240 shares on day 3rd and 10th respectively

5)the graph has moved 45 unit up

6)Amber's posts will travel fastest

7)Amber' function

Step-by-step explanation:

1)

Ben shares posts with two friends and then they share with 3 more everyday, so her the growth rate is 3

f(x)=2(3)^x

x=number of days

2)

Carter shares posts with ten friends and then they share with 2 more everyday, so her the growth rate is 2

f(x)=10(2)^x

x=number of days

3)

Graph attached contain graph's of following

Ben's f(x)=2(3)^x in red

Carter's f(x)=10(2)^x in blue

Amber's f(x)=3(4)^x in green

4)

Finding how many shares each student will get on day 3 and day 10:

For Amber:

substituting x=3,

f(x)=3(4)^3

     = 192

Now substituting x=10,

f(x)= 3(4)^10

     = 3145728

Amber will have 192 and 3145728 shares on day 3rd and 10th respectively

For Ben:

substituting x=3,

f(x)=2(3)^3

     = 54

Now substituting x=10,

f(x)= 2(3)^10

     = 118,098

Ben will have 54 and 118,098 shares on day 3rd and 10th respectively

For Carter:

substituting x=3,

f(x)=10(2)^3

     = 80

Now substituting x=10,

f(x)= 10(2)^10

     = 10240

Carter will have 80 and 10240 shares on day 3rd and 10th respectively

5)

If Amber's graph changes to

f'(x)=3(4)^x +45

then as per translation, it means the graph has moved 45 unit up from original position as shown in attached graph

original f(x)=3(4)^x in green

translated f'(x)=3(4)^x +45 in blue

6)

In exponential function the base of function effects the growth and in given cases of Amber, Ben and Carter; base of Amber's function is greatest i.e 4 other two have 2 and 3.

So Amber's posts will travel fastest

7) A post with fewer friends initially and then more shares like Amber. Because at the end of the day the growth rate is important and as explain above the number of shares i.e base of exponential function is important.

Hence for more shares and likes Amber' function is the best choice !

hey seth! : )

i’m not 100% sure, but i think it’s b

hope this ya : p

miss u!

- nicole