A country commits to decreasing spending for infrastructure in various ways at a rate of 30 percent per year. At the time of the announcement, the country is spending 12 dollars billion per year. Which graph models the amount of infrastructure spending for future years?
Answer
A
Image with description On a coordinate plane, the x-axis ranges from negative 20 to 20 in increments of 5, and the y-axis ranges from 0 to 100 in increments of 10. A smooth curve goes up and to the right and passes through the labeled point 0 comma 30, and the point 10 comma 90.
B
Image with description On a coordinate plane, the x-axis ranges from negative 20 to 20 in increments of 5, and the y-axis ranges from 0 to 100 in increments of 10. A smooth curve goes down and to the right and passes through the point negative 5 comma 70, and the labeled point 0 comma 12.
C
Image with description On a coordinate plane, the x-axis ranges from negative 20 to 20 in increments of 5, and the y-axis ranges from 0 to 100 in increments of 10. A smooth curve goes up and to the right and passes through the labeled point 0 comma 12, and the point 5 comma 45.
D
Image with description On a coordinate plane, the x-axis ranges from negative 20 to 20 in increments of 5, and the y-axis ranges from 0 to 100 in increments of 10. A smooth curve goes down and to the right and passes through the point negative 5 comma 55, and the labeled point 0 comma 30.
Explanation
A 30% decrease each year means spending is multiplied by 1 − 0.30 = 0.70 each year. Starting at 12 billion, the model is y = 12(0.70)^t, so it begins at (0, 12) and decreases as time moves forward. Choice B shows a decreasing curve with a y-intercept of 12 billion.
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