Shell's the art director at her local community center. she paod $10 and for each child that attends she earns $4. graph and label the relationship on the grid.

shell's the art director at her local community center. she paid $10 and for each child that attends she earns $4.

for each child she ears $4 that is the slope m = 4

she paid $10, that is the initial amount paid. so 10 is the y intercept b

m =4   and b = 10

y intercept is 10 so the point is (0,10)

we start graph from y intercept (0,10)

slope = 4 . we know slope = rise / run

slope = 4   or 4/1   are same

rise = 4   and run = 1

for rise we move 4 units up and for run we move 1 unit to the right

the graph is attached below

x axis is the number of child she attends

y axis is the amount   she earns

the given function is:

f(m) = 4 (1.08)^m
part a:  
solve m when f(m) = 6.86

6.86 = 4 (1.08)^m
divide both sides by 4:
(1.08)^m = 6.86 / 4 
apply log to both sides :

m log(1.08) = log (6.86 / 4)
m = log (6.86 / 4) / log(1.08)

m = 7 months
therefore the study concluded after 7 months.
domain = [6.86, 7] 

now solve for f(m) when m = 0

f(m) = 4 (1.08)^0

f(m) = 4

therefore the initial length is 4 cm.

domain = [4, 0]

a reasonable domain is between [4, 0] to [6.86, 7]  .
part b: the y-intercept is the value of the f(m) when m = 0, so it represents the initial length of the fish at day 0. the y-intercept is:

f(m) = 4 (1.08)^0

f(m) = 4

part c:  
average rate of change = change in the radius / change in days
average rate of change = [ f(7) - f(3) ] / (7 - 3) = [4 (1.08)^7 - 4 (1.08)^3] / (7)
average rate of change = 1.816 / 7 
average rate of change = 0.26 cm / month

this represents the growth per month.