The number of people waiting in line to buy a new piece of technology is measured by the differentiable function f, where f(t) is measured in people and t is measured in minutes after the store opened. What are the units of f^(')(t) ? minutes people minutes / person people / minute minutes / person ^(2) people / minute ^(2)

Question

The number of people waiting in line to buy a new piece of technology is measured by the differentiable function  f, where  f(t) is measured in people and  t is measured in minutes after the store opened. What are the units of  f^(')(t) ? minutes people minutes / person people / minute minutes / person  ^(2) people / minute  ^(2)

Bytelearn · Accepted Answer

Understand f(t) and f'(t): Understand the function f(t) and its derivative f'(t). The function f(t) represents the number of people waiting in line, measured in people, and t represents the time after the store opened, measured in minutes. The derivative f'(t) represents the rate of change of the number of people with respect to time.Determine Derivative Units: Determine the units of the derivative f'(t). Since f(t) is measured in people and t is measured in minutes, the derivative f'(t) will measure the change in people (number of people) per change in time (minutes). Therefore, the units of f'(t) will be the units of f divided by the units of t.Write f'(t) Units: Write down the units of f'(t). The units of f(t) are people, and the units of t are minutes. Thus, the units of f'(t) are people per minute.

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