wine market continues to grow and using recent data
w(t)=9.70t+300
where t is the number of years past 2000 and
W(t) is in millions of cases
They should not be using both w and W. Pick one or the other.
I'll use big W because, for example, W(17) = 465 means 465 Million cases of wine consumed in 2017! 
I am completely unfamiliar with this format. I have a list of questions looking for how many cases were consumed in 2002, what is the increase decrease in consumption per year and interpret the y-intercept. We have been working on cost functions and profit functions but I dont have any other previous work with this function. Can someone help me with a format?
I am looking for help as to what these numbers represent
The equation W(t)=9.70t+300 is a linear equation (its graph is a straight line).
The symbol W(t) is called function notation. It's just a different way of writing y. The W is the name of the function. The input variable (aka: independent variable, free variable) is shown inside the parentheses.
y = W(t) = 9.70t + 300
If we were to report, for example, y = 309.7, it tells us that wine consumption was 309.7 million cases, but it doesn't speak to
when. By giving symbol y a new name, using function notation, we get more information and we don't confuse different y symbols from different functions with one another. Each function has its own name.
Writing W(1) = 309.7 tells us those 309.7 million cases were consumed in 2001 (because the value of t shown inside the parentheses means one year after 2000).
The given equation W(t)=9.70t+300 is a formula. We can use it for finding values of y (i.e., W). If we have a value for t, then W is 9.7 times that value, plus 300 more.
The constant 9.70 represents the rate at which W (wine consumption) grows each year. In your exercise, it's an average growth rate that's valid for some number of years after 2000, and it does not change.
In other words, after the year 2000, wine consumption increased at a rate of 9.7 million cases per year. (Each year's consumption was 9.7 million more than the year before.)
The constant 300 is the "initial" consumption. That is, it's the consumption at time zero (the year 2000).
W(0) = 9.70(0) + 300 = 300 million cases consumed in the year 2000
Let's find the wine consumption (according to this model) for last year. 2016 is 16 years after 2000, so t=16.
W(16) = 9.70(16) + 300
W(16) = 455.2 million cases of wine consumed in the year 2016
We could find the number of cases consumed halfway through 2005.
W(5.5) = 9.70(5.5) + 300
W(5.5) = 353,350,000 cases of wine consumed by the end of June in 2005.
We could be given a value for W(t), and asked to find when.
W(t) = 387.3
We would use algebra to solve the equation 387.3 = 9.70t + 300 for t, thus finding the year corresponding to that consumption as 2005.
Students spend months learning about linear relationships between quantities.
y = m*x + b
x = input variable
y = output variable
m = slope (rate)
b = y-intercept (point where the line crosses the vertical axis -- happens when x=0)
You can find thousands of lessons, worked examples, graphs, videos, etc. on-line. Start by googling the phrase
linear equation examples.
