Exponential Functions — Test

Question 12 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

Which graph is the sequence defined by the function f of x is equal to 3 times 2 raised to the x minus 1 power ?

Answer

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 1 comma 2, a point at 2 comma 6, a point at 3 comma 18, a point at 4 comma 54, and a point at 5 comma 162.

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 0 comma 2, a point at 1 comma 6, a point at 2 comma 18, a point at 3 comma 54, and a point at 4 comma 162.

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 1 comma 3, a point at 2 comma 6, a point at 3 comma 12, a point at 4 comma 24, and a point at 5 comma 48.

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are six points plotted on the plane showing an increasing exponential trend, a point at 0 comma 3, a point at 1 comma 6, a point at 2 comma 12, a point at 3 comma 24, a point at 4 comma 48, and a point at 5 comma 96.

Explanation

The function is f(x) = 3 · 2^(x − 1). Starting at x = 1 gives f(1) = 3 · 2^0 = 3; each increase of 1 in x doubles the value, giving the points (1, 3), (2, 6), (3, 12), (4, 24), and (5, 48). These points match choice D.

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