You own two restaurants. From 1995 to 2000, the sales R1 (in thousands of dollars) for one restaurant can be modeled by:

R1 = 480 – 8t – 0.8t2, t = 0, 1, 2, 3, 4, 5, where t = 0 represents 1995.
During the same 6-year period, the sales R2 (in thousands of dollars) for the other restaurant can be modeled by:
R2 = 254 + 0.78t, t = 0, 1, 2, 3, 4, 5
Write a function R3 that represents the total sales for the two restaurants.

clearly, R3 = R1+R2

To find the function R3 that represents the total sales for the two restaurants, we need to calculate the sum of the sales for each restaurant at each corresponding time period.

Let's break it down step by step:

1. Determine the sales for restaurant R1 at each time period.
- Using the given model, for each value of t from 0 to 5, substitute it into the equation R1 = 480 – 8t – 0.8t^2 and calculate the result.

For t = 0, R1 = 480 – 8(0) – 0.8(0^2) = 480.
For t = 1, R1 = 480 – 8(1) – 0.8(1^2) = 471.2.
For t = 2, R1 = 480 – 8(2) – 0.8(2^2) = 459.2.
For t = 3, R1 = 480 – 8(3) – 0.8(3^2) = 444.4.
For t = 4, R1 = 480 – 8(4) – 0.8(4^2) = 426.4.
For t = 5, R1 = 480 – 8(5) – 0.8(5^2) = 405.

2. Determine the sales for restaurant R2 at each time period.
- Using the given model, for each value of t from 0 to 5, substitute it into the equation R2 = 254 + 0.78t and calculate the result.

For t = 0, R2 = 254 + 0.78(0) = 254.
For t = 1, R2 = 254 + 0.78(1) = 254.78.
For t = 2, R2 = 254 + 0.78(2) = 255.56.
For t = 3, R2 = 254 + 0.78(3) = 256.34.
For t = 4, R2 = 254 + 0.78(4) = 257.12.
For t = 5, R2 = 254 + 0.78(5) = 257.9.

3. Calculate the total sales for each time period.
- Add the values of R1 and R2 at each time period to get the total sales, which will give us the values for R3.

For t = 0, R3 = R1 + R2 = 480 + 254 = 734.
For t = 1, R3 = R1 + R2 = 471.2 + 254.78 = 725.98.
For t = 2, R3 = R1 + R2 = 459.2 + 255.56 = 714.76.
For t = 3, R3 = R1 + R2 = 444.4 + 256.34 = 700.74.
For t = 4, R3 = R1 + R2 = 426.4 + 257.12 = 683.52.
For t = 5, R3 = R1 + R2 = 405 + 257.9 = 662.9.

Therefore, the function R3 that represents the total sales for the two restaurants is:
R3 = { 734, 725.98, 714.76, 700.74, 683.52, 662.9 }.