Quadratic Functions — Test

Question 21 • Mathematics I

A function models the growth of a sample starting with 40 bacteria with the ability to double every two hours. Which graph models the function?

Answer

Image with description On a coordinate plane, the x-axis ranges from negative 0.5 to 0.5 in increments of one-tenth, and the y-axis ranges from 0 to 1,000 in increments of 100. A smooth curve goes down and to the right and passes through the point negative 0.3 comma 500 and the labeled point 0 comma 2.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 5 in increments of 1, and the y-axis ranges from 0 to 1,200 in increments of 100. A smooth curve goes down and to the right and passes through the point negative 9 comma 900 and the labeled point 9 comma 40.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 10 in increments of 1, and the y-axis ranges from 0 to 1,200 in increments of 100. A smooth curve goes up and to the right and passes through the labeled point 0 comma 40 and the point 9 comma 900.

Image with description On a coordinate plane, the x-axis ranges from negative 0.5 to 0.5 in increments of one-tenth, and the y-axis ranges from 0 to 1,000 in increments of 100. A smooth curve goes up and to the right and passes through the labeled point 0 comma 2 and the point 0.3 comma 500.

Explanation

The sample starts with 40 bacteria, so the graph must pass through (0, 40). Since the number doubles every two hours, it grows as time increases. After 9 hours, the model gives 40 × 2^(9/2), which is about 905 bacteria, matching the point near (9, 900). Choice C is the increasing graph with these features.

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