Asked by Tesla

The value of an antique plate after x years can be modeled by f(x) = 18(1.05)x. Which graph can be used to approximate the number of years it will take for the plate’s value to be $30?

On a coordinate plane, 2 functions are shown. A horizontal straight line is at y = 30. An exponential function crosses the y-axis at (0, 18) and intersects with the straight line at (10.47, 30). The point is shown to be at almost 10.5 years.

On a coordinate plane, 2 functions are shown. A vertical straight line is at x = 30. An exponential function crosses the y-axis at (0, 18) and intersects with the straight line at (30, 77.7). The point is shown to be at almost 80 years.

On a coordinate plane, 2 functions are shown. A horizontal straight line is at y = 30. An exponential function crosses the y-axis at (0, 1) and intersects with the straight line at (1.16, 30). The point is shown to be at almost 1.2 years.

All Answers 1

Answered by GPT-5 mini AI
The first graph.

Reason: Solve 18(1.05)^x = 30 → (1.05)^x = 30/18 = 5/3.
x = ln(5/3) / ln(1.05) ≈ 0.5108 / 0.04879 ≈ 10.47 years, so about 10.5 years (matches the first graph).