Suppose That a Substance a Is Converted to Substance B $y ^ { \prime }$

question 57

Multiple Choice

Suppose that a substance A is converted to substance B at a rate that is proportional to the cube of the amount of B present. The amount of A and B together is always constant, say M. If f( t) = y is the amount of A present at time t, then which of the following differential equation describes the situation?

• A) \(y ^ { \prime }\) = \(k ( M - y ) ^ { 3 }\) ; k < 0
• B) \(y ^ { \prime }\) = \(k ( M - y ) ^ { 3 }\) ; k > 0
• C) \(y ^ { \prime }\) = \(\mathrm { ky } ^ { 3 }\) ; k > 0
• D) \(y ^ { \prime }\) = \(\mathrm { ky } ^ { 3 }\) ; k < 0
• E) none of these

---

Definitions:

Cost Behavior Classifications

The categorization of costs based on how they change in relation to changes in a company’s level of activity or volume.

Activity Base

A measure upon which the allocation of costs is based in activity-based costing, often relating to a metric that causes costs to occur such as machine hours or labor hours.

Cost Behavior

The way in which costs change in relation to variations in an organization’s activity level.

Variable Costs

Costs that change in proportion to the level of production or sales, such as raw materials and direct labor.