Vocabulary: Match each of the vocabulary words with the correct definitions. riserun
y2-y1x2-x1
Rate of Change
b
m
when the value of x is 0
when the line crosses the y-axis
horizontal line
vertical line
increasing line
Decreasing line
all rates of change are the same
y = mx + b
any form of ax + by + c = 0

Vocabulary Word Options:
Undefined slope
Positive slope
Negative slope
Slope
The letter that represents the y-intercept
The letter that represents slope
Slope of a Graph
Slope of a Table
Y-intercept
Zero slope
Y-intercept of a graph
Linear equation
Slope intercept form
Standard form

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part a: 1.08

part b: 27.59

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.

oof. u are asking for t much