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.
Assuming you meant:
480 - 8t - .8t^2 or R1
sub in all the values of t into R1, then add them up
sub in all the values of t into R2, then add them up
compare the two answers.
To find the total sales for the two restaurants, you can simply add the sales of the first restaurant (R1) and the sales of the second restaurant (R2) for each given year.
Let's denote the total sales as R3. Thus, the function R3 can be written as:
R3 = R1 + R2
Substituting the given expressions for R1 and R2, we have:
R3 = (480 – 8t – 0.8t^2) + (254 + 0.78t)
Simplifying this equation, we get:
R3 = 480 – 8t – 0.8t^2 + 254 + 0.78t
Combining like terms, we have:
R3 = (480 + 254) + (-8t + 0.78t) – 0.8t^2
Further simplifying, we get:
R3 = 734 – 7.22t – 0.8t^2
Therefore, the function R3 that represents the total sales for the two restaurants is:
R3 = 734 – 7.22t – 0.8t^2
To find the total sales for the two restaurants, we need to add the sales of each restaurant, R1 and R2, for each given value of t.
Given the equations:
R1 = 480 – 8t – 0.8t^2
R2 = 254 + 0.78t
To find the total sales, we need to calculate R3, which is the sum of R1 and R2.
R3 = R1 + R2
Substituting the equations for R1 and R2 into R3, we get:
R3 = (480 – 8t – 0.8t^2) + (254 + 0.78t)
Expanding and combining like terms, we simplify the equation:
R3 = 480 + 254 - 8t + 0.78t - 0.8t^2
Simplifying further:
R3 = 734 - 7.22t - 0.8t^2
Therefore, the function R3 that represents the total sales for the two restaurants is:
R3(t) = 734 - 7.22t - 0.8t^2