Comparing Exponential, Linear, and Quadratic Growth — Quiz

Question 8 • Algebra I

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

Answer

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 2) and (1 comma 2). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 4) and (1 comma 4). The curve goes through (0 comma 1), (1 comma 2), (2 comma 4), and (3 comma 8).

Image with description On a coordinate plane, the x axis lists negative 1 to 5 by 1 unit. The y axis lists negative 2 to 8 by 1 unit. The parabola opens up, has vertex at the origin, and passes through (2 comma 2) and (4 comma 8). The curve goes through (0 comma 1) and (1 comma 4).

Image with description On a coordinate plane, the x axis ranges from negative 1 to 5 with an interval of 1 unit. The y axis ranges from negative 2 to 8 with in interval of 1 unit. The parabola opens up, has vertex at the origin, and passes through (negative 1 comma 3) and (1 comma 3). The curve goes through the origin, (1 comma 1), (2 comma 3), and (3 comma 7).

Explanation

In choice C, the quadratic passes through (2, 2) and (4, 8), so it is y = 0.5x². The exponential passes through (0, 1) and (1, 4), so it is y = 4ˣ. Over 0 ≤ x ≤ 5, 4ˣ increases more rapidly than 0.5x²; for example, by x = 5 the exponential is 1,024 while the quadratic is 12.5. Thus, the pair in choice C fits.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz