A Mold Culture in a Dorm Refrigerator Is Circular and Growing

question 20

Multiple Choice

A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.1 cm/day. How fast is the area growing when the culture is 6 centimeters in radius (The area of a disc of radius r is $A = \pi r ^ { 2 }$ .)

• A) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 18 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• B) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 0.6 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• C) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 2.4 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• D) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 1.2 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• E) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 0.2 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)

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Definitions:

Compounded Semi-Annually

The process of adding interest to the principal sum twice a year, where interest earns more interest in subsequent periods.

Compounded Quarterly

Interest is calculated four times a year on the initial principal and the added interest from previous periods.

20 Years

A period or duration of two decades.

Compounded Monthly

A term referring to the calculation of interest on the initial principal and also on the accumulated interest from previous periods, computed each month.