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.



A.
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.


B.
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.


C. 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.


D.
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.

Answer 1

B

Reason: a(t)=1000(1.09)^t is exponential growth. After 10 years a(10)=1000(1.09)^10 ≈ 1000(2.368) ≈ $2,369, so the correct graph is an increasing curve that extends above $2,000 — option B.