Question

In 1990, the profit of the Gamma company was $10,512,549. Each year after 1990, profits fell by $28,452 on average. Construct a linear model for this scenario and use it to solve for the profits in the year 2020.

a) $8,352,549
b) $5,712,549
c) $4,500,000
d) $6,000,000

Answer 1

To find Gamma company's profits in 2020, a linear model P(x) = 10,512,549 - 28,452x was constructed using the initial profit and the annual decrease. By substituting x = 30 for the year 2020, the calculated profit was $9,658,989, which doesn't match the provided options.

Step-by-step explanation:

The student is asking how to construct a linear model to represent the yearly decline in profits for Gamma company from 1990 to 2020 and to find the profits in the year 2020. First, we identify the initial profit in 1990 as $10,512,549 and the average annual decrease as $28,452. We represent years since 1990 with the variable x, where x = 0 corresponds to 1990. The linear model describing this situation is P(x) = 10,512,549 - 28,452x, where P(x) is the profit in the year 1990+x.

Now, to find the profits in the year 2020, we calculate the value of x for 2020, which is 2020 - 1990 = 30. Plugging this into the model gives us P(30) = 10,512,549 - 28,452(30). A quick calculation shows P(30) = 10,512,549 - 853,560, which simplifies to $9,658,989. This is not one of the options provided, indicating there may have been an error in the options, or the original problem. The closest option to the correct answer is option c.