If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y , the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x ?
Answer
A
Image with description A coordinate plane titled Growth of Flowering Tree shows age of tree in years labeled 1 to 10 on the x-axis and number of blossoms labeled 50 to 500 in increments of 50 on the y-axis. A scatter plot shows the number of blossoms declining from approximately 400 at age 1 to approximately 275 at age 3, approximately 225 at age 4, approximately 160 at age 5, approximately 100 at age 6, approximately 80 at age 7, approximately 65 at age 8, approximately 60 at age 9, and approximately 55 at age 10.
B
Image with description A coordinate plane titled Growth of Flowering Tree shows age of tree in years labeled 1 to 10 on the x-axis and number of blossoms labeled 50 to 500 in increments of 50 on the y-axis. A scatter plot shows the number of blossoms starting at approximately 450 at age 2, rising slightly to approximately 475 at age 3, then declining to approximately 450 at age 4, approximately 350 at age 5, approximately 200 at age 6, and approximately 50 at age 7.
C
Image with description A coordinate plane titled Growth of Flowering Tree shows age of tree in years labeled 1 to 10 on the x-axis and number of blossoms labeled 50 to 500 in increments of 50 on the y-axis. A scatter plot shows the number of blossoms rising steadily from approximately 25 at age 1 to approximately 60 at age 2, approximately 75 at age 3, approximately 100 at age 4, approximately 110 at age 5, approximately 150 at age 6, approximately 175 at age 7, approximately 200 at age 8, approximately 225 at age 9, and approximately 250 at age 10.
D
Image with description A coordinate plane titled Growth of Flowering Tree shows age of tree in years labeled 1 to 10 on the x-axis and number of blossoms labeled 50 to 500 in increments of 50 on the y-axis. A scatter plot shows the number of blossoms starting at approximately 25 at age 1, staying at approximately 25 at age 2, then rising steadily to approximately 50 at age 3, approximately 100 at age 4, approximately 110 at age 5, approximately 175 at age 6, approximately 260 at age 7, and approximately 450 at age 8.
Explanation
Exponential growth increases by larger amounts as time passes, creating an upward curve that gets steeper. In graph D, blossoms rise from about 25 at year 2 to 50 at year 3, 100 at year 4, and then continue increasing more rapidly, reaching about 450 by year 8. Graph C rises at a steadier, roughly linear rate, so D best represents exponential increase.
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