Question

Callie entered an art contest in second grade and won a $1,000 scholarship. The money was invested in an account paying a 9% interest rate compounded annually. The situation can be modeled by the equation a(t)=1,000(1.09)^t
, where a is the amount in the account after t years. If Callie uses the scholarship 10 years later, determine which graph accurately displays the situation.(1 point)

A decreasing curve with a point at the end is plotted in the first quadrant of a coordinate plane. The x axis ranges from 0 to 10 in increments of 1 and the y axis ranges from 0 to 1200 in increments of 200.
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The approximate coordinates through which the curve passes are left parenthesis 0 comma 1,000 right parenthesis, left parenthesis 1 comma 90 right parenthesis, left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 0.7 right parenthesis, and left parenthesis 4 comma 0.07 right parenthesis. As the x values increase, the y values continue to approach 0.

Image Long Description


An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 14 in increments of 2 and the y-axis ranges from 0 to 3,500 in increments of 500.
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The approximate coordinates through which the curve passes are left parenthesis 0 comma 1,000 right parenthesis, left parenthesis 8 comma 1,990 right parenthesis, left parenthesis 12 comma 2,810 right parenthesis, and left parenthesis 14 comma 3,340 right parenthesis.

Image Long Description


A decreasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 12 in increments of 2 and the y-axis ranges from 0 to 1,200 in increments of 200.
▼Click for Long Desc
The approximate coordinates through which the curve passes are left parenthesis 0 comma 1,000 right parenthesis, left parenthesis 2 comma 830 right parenthesis, left parenthesis 4 comma 690 right parenthesis, left parenthesis 6 comma 570 right parenthesis, left parenthesis 8 comma 470 right parenthesis, left parenthesis 10 comma 390 right parenthesis, and left parenthesis 12 comma 320 right parenthesis.

Image Long Description


An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 5 in increments of 1 and the y-axis ranges from 0 to 2000 in increments of 500.
▼Click for Long Desc
The approximate coordinates through which the curve passes are left parenthesis 0 comma 1,000 right parenthesis, left parenthesis 2 comma 1,190 right parenthesis, left parenthesis 3 comma 1,300 right parenthesis, and left parenthesis 4.7 comma 1,500 right parenthesis.

Image Long Description

Answer 1

The second graph (the increasing curve with x from 0 to 14 and y to 3500).

Reason: a(t)=1000(1.09)^t is exponential growth. After 10 years a(10)=1000(1.09)^10 ≈ 1000(2.367) ≈ $2,367, which matches the scale and points shown in that graph.