Final answer:
To predict the year when the income will reach $1000 using the linear model, calculate the slope of the line, use a point-slope form equation, and solve for the year. The predicted year is 2531, the closest option is 2026.
Step-by-step explanation:
To predict the year when the income will reach $1000 using the linear model, we need to determine the equation of the line and solve for the year.
From the given information, we can calculate the slope of the line using the formula: slope = (change in income) / (change in year). Let's use the two data points provided:
(1985, 25.52) and (1990, 34.275).
slope = (34.275 - 25.52) / (1990 - 1985) = 8.755 / 5 = 1.751
Now that we know the slope, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line. Let's use (1985, 25.52) as our point:
y - 25.52 = 1.751(x - 1985)
Finally, we can substitute y = 1000 and solve for x to determine the year:
1000 - 25.52 = 1.751(x - 1985)
974.48 = 1.751x - 3466.735
1.751x = 4441.215
x ≈ 2531.32
Since the year is in decimal form, we need to round it to the nearest whole number.
The predicted year when the income will reach $1000 is 2531. Let's look at the options provided to find the closest year:
2023
2024
2025
2026
The closest year is 2026, so the answer is d) 2026.