Project: applications of sequences sara, sam and shannon spent the summer at sleep away camp. their goal for the summer was to get the campers to donate a part of their free time during each session participating in community service activities. the progress of their goal was recorded by the number of hours the campers participated in community service activities each session. the data table below shows the campers' efforts. x f(x) 1 14 2 23 3 32 4 41 5 50 6 59 1. write an description relating the variables, x and f(x), to the quantities in the table. 2. create a graph of the data. label the axes appropriately. 3. the data shows a pattern between the number of community service hours and camp session. is the pattern arithmetic? what process can sara, sam and shannon follow to find the difference in the number of community service hours for each camp session? 4. write an explicit formula that represents the data in the table. use function notation in your final formula. 5. sara, sam and shannon predict how many community service hours will be dedicated during the 10th camp session.

The modeled equation for this table is f(x) = 9x + 5.

Creating this model allows you to solve the other parts of your project. In order to find this equation, you need to start by finding the slope. Slope (m) can be found by using two points in the slope equation listed below.

m = (y1 - y2)/(x1 - x2)

We'll use the first two points for this equation.

m = (23 - 14)(2 - 1)

m = 9/1

m = 9

Now that we have slope, we can plug into the slope intercept form (y = mx + b) along with any ordered pair to find the y-intercept (b)

y = mx + b

14 = 9(1) + b

14 = 9 + b

5 = b

So knowing those two things allows us to write an equation as y = 9x + 5.

If you use this equation, you'll be able to graph like they ask in part 2. The process we followed is step 3. The equation is step 4. That leaves us with just finding what the 10th week will give. Since x stands for weeks, we can just use x = 10 to find f(x).

f(x) = 9x + 5

f(x) = 9(10) + 5

f(x) = 90 + 5

f(x) = 95

black/brown

step-by-step explanation:

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