Question

Please Help Ill Give Medal and Fan U!!!!!!!



Stacey is studying the sale of a particular brand of cereals from the year 1995 to 2004. She writes the following function to model the sale of the cereal S(t), in million dollars, after t years:
S(t)= t^2 +6t+48

Part A: What does the y-intercept of the graph of the function represent?

Part B: What is the reasonable domain of the graph of the function?

Part C: What is the average rate of change of the sale of the cereal from the first year to the fourth year?

Answer 1

The y-intercept will be the +48 at the end of the function, so that takes care of Part A.

Answer 2

What do u mean by +48

Answer 3

The function is S(t)= t^2 +6t+48, the y-intercept will always be the last number if it's in that form.

Answer 4

+48 is at the end the '+' just indicates that the '48' is a positive number, and not a negative.

Answer 5

ohhh ok thanks.

Answer 6

(That's Part B)

Answer 7

Sorry let me correct that..

Answer 8

that's fine go ahead.

Answer 9

The domain should be 0<t<183, because Stacey is studying between the years 1995-2004, which is 9 years. On your graph S(t)= t^2 +6t+48, when t(years) = 9, y = 183. So 183 would be your highest, and 0 would be your lowest, because you cannot have negative sales of cereal.

Answer 10

We're dealing with 't' not 'x' for the variable.

Answer 11

I see.

Answer 12

To find the average rate of change from year 1 to year 4, just plug in 1 and 4 for t, in the equation:

S(t) = t^2 + 6t + 48
S(1) = (1)^2 + 6(1) + 48
S(1) = 1 + 6 + 48
S(1) = 7 + 48
S(1) = 55

So year 1 = 55.

S(t) = t^2 + 6t + 48
S(4) = (4)^2 + 6(4) + 48
S(4) = 16 + 24 + 48
S(4) = 40 + 48
S(4) = 88

So year 4 = 88

Now we can plug in our values (1, 55) and (4, 88) into the slope equation:

m = y2 - y1 / x2 - x1

y2 = 88
y1 = 55
x2 = 4
x1 = 1

m = 88 - 55 / 4 - 1
m = 33 / 3
m = 11

So the average rate of change from year 1 to year 4 is 11.

Answer 13

And that's Part C.