A sign containing 50 m^2 of printed material is required to have margins of 4 m at the top and
bottom and 2 m on each side.
a. Find a mathematical model expressing the total area of the sign as a function of the horizontal
dimension of the region covered by the printed material.
b. What is the domain of your function in part (a)?
a. To find the total area of the sign, we need to subtract the margins from the horizontal dimension of the region covered by the printed material.
Let's call the horizontal dimension of the region covered by the printed material "x".
The total area of the sign can be calculated by adding the area of the printed material to the area of the margins. The area of the printed material is simply the product of the length and width: x m multiplied by 50 m^2.
The area of the top margin is 4 m multiplied by x m, and the area of the bottom margin is also 4 m multiplied by x m. The area of the side margins is 2 m multiplied by 2 m, since there are two side margins.
Therefore, the mathematical model expressing the total area of the sign as a function of the horizontal dimension (x) is:
Total Area = (x * 50) + (2 * 2) + (4 * x) + (4 * x)
Simplifying this equation, we get:
Total Area = 50x + 4x + 4x + 4x + 4
b. The domain of the function in part (a) is the set of all possible values for the horizontal dimension (x). Since the dimensions of a sign cannot be negative, x must be greater than or equal to 0. Therefore, the domain of the function is x ≥ 0.