Answer:
Part 1) The rate of change is
Part 2) The initial value is 68
Part 3) The function rule to the linear model is 
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to

where
m is the slope or unit rate
b is the y-intercept or initial value
step 1
Find the slope
take two points from the table
(0,68) and (15,85)
The formula to calculate the slope between two points is equal to
substitute the values
In a linear function , the slope is the same that the rate of change
therefore
The rate of change is
step 2
Find the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
Looking at the table
For x=0, y=68
therefore
The y-intercept is
The y-intercept is also called the initial value
therefore
The initial value is 68
step 3
Determine the function rule to the linear model

we have
substitute

4k+6 is greater or equal to -14
4k is greater or equal to -20
k is greater or equal to -5 <-- answer
The answer to this question is a=2
We have that the probability of Janice rolling a 2 or 5 on her 7th toss of the dice is

From the question we are told that
Janice rolled either a 2 or a 5 on the last 6 rolls of the die
Janice rolling a 2 or 5 on her 7th toss of the dice

Where

Janice roll the standard die 7th time the probability of getting 2 or 5 is

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Answer: <
Step-by-step explanation: The top triangle (1) has a smaller area than triangle 2.