The output values of linear function C(x) = s + px for 1 ≤ x ≤ 8 give the possible costs for these items, in dollars
Which of the following give the possible costs for these items?
The potential costs for the items, a shovel, and plants for a new garden can be represented by different mathematical models.
All the options represent potential models for calculating the total cost of the shovel and plants for a garden. The actual choice depends on the specific cost structure, whether the cost increases linearly, exponentially, or through an arithmetic or geometric sequence with each additional plant.
However, the most appropriate option for determining the possible costs for the shovel and plants, given the scenario, would be the linear function:
C(x) = s + px for 1 ≤ x ≤ 8
The reason is that a linear function provides a straightforward and intuitive relationship where the cost of the items (shovel and plants) increases linearly with the number of plants. This aligns with the scenario described, where the cost of the shovel (s) is added to the product of the cost per plant (p) and the number of plants (x).
A family needs to buy one shovel and between one and eight plants, inclusive, for their new garden. The cost of the shovel is & dollars, and the cost of one plant is p dollars. The output values of which of the following give the possible costs for these items, in dollars? (Note: Assume any taxes are included in the costs.)
A. The linear function C(x)=s+pxfor1≤ x≤ 8
B. The exponential function C(x)=s· p^x for 1≤ x≤ 8
C. The arithmetic sequence C_n=s+pn for 1≤ n≤ 8
D. The geometric sequence C_n=s· p^n for 1≤ n≤ 8