1. The scatterplot above shows the amount of United States exports of trade goods to Australia in selected years from 1985 to 2015. Also shown is a trend line for the data with equation y = 0.65x + 4.6, which is used to predict the amount, y, in billions of dollars, of United States exports of trade goods to Australia x years after 1985. Based on the equation of the trend line, what is the predicted amount of United States exports to Australia, in billions of dollars, in the year 2030?
Answer: D
The predicted amount of United States exports to Australia in the year 2030 is 33.85 billion dollars.
To find the predicted amount of United States exports to Australia in 2030, we substitute x = 45 into the trend line equation y = 0.65x + 4.6. This calculation results in an estimated export value of 33.85 billion dollars.
A) 24.1
This option is incorrect because substituting x = 45 into the equation y = 0.65(45) + 4.6 gives a much higher value than 24.1. The correct calculation yields a predicted amount of 33.85 billion dollars, making this option significantly lower than the actual prediction.
B) 27.35
This option is also incorrect as it is not supported by the trend line equation. When calculating y for x = 45, the result is higher than 27.35, specifically 33.85 billion dollars, indicating that this estimate underrepresents the predicted exports.
C) 30.6
This option is incorrect as well. The predicted amount calculated from the equation for the year 2030 (x = 45) results in 33.85 billion dollars, which is greater than 30.6. Hence, this option does not accurately reflect the trend line's prediction.
D) 33.85
This option is correct. By substituting x = 45 into the trend line equation y = 0.65x + 4.6, we find that the predicted exports to Australia in 2030 amount to 33.85 billion dollars, making this the accurate choice based on the provided data.
E) 37.1
This option is incorrect as it exceeds the predicted value calculated from the trend line. The equation gives a maximum predicted amount of 33.85 billion dollars for the year 2030, making 37.1 an unrealistic estimation based on the trend.
Conclusion
The correct answer is definitively 33.85 billion dollars, as it is directly derived from the trend line equation for the year 2030. All other options fail to represent the accurate prediction, either being significantly lower or higher than the calculated value, thereby confirming their inaccuracy in relation to the provided data.