A firm is phasing out an old product line. The production level is reduced by 100 units in the first week, by an additional 150 units in the second week, and by an additional 200 units in the third week. If this trend of accelerating reduction continues, which term best describes the mathematical shape of the function representing the product's remaining production level over time?

Analyzing Production Shutdown Data

If a function is both decreasing and concave, its curve becomes less steep as the input variable increases.

For a function that is both decreasing and concave, match each characteristic of the function to its correct mathematical description.

Interpreting Functional Properties

Modeling with Decreasing Concave Functions

A company's quarterly profit is declining. The statements below describe the amount of profit lost in three consecutive quarters. Arrange these events in a sequence that would define the company's total profit over time as a concave and decreasing function.

A function that is both decreasing and concave models a rate of change that is negative and becomes even more negative as the input value increases. This implies that the curve representing the function becomes progressively _______ as the input value grows.

A company is tracking the declining market share of one of its products. The data collected over five consecutive months is shown below:

• Month 1: 20%
• Month 2: 18%
• Month 3: 15%
• Month 4: 11%
• Month 5: 6%

Based on this data, which of the following best describes the function representing the market share over time?

Evaluating Pollution Reduction Models