Ursula is starting a new national network of science fiction book clubs. The establishment and expansion of the network is as follows. The original network began with eight people in each club and four clubs in each of two states. Every month, the number of people in each club increases by two and the number of clubs in each state grows by one. The number of states where the groups exist also increases by one every month. The total number of people in the network of book clubs is represented by the expression below, where x is the number of months since the clubs were established.

Ursula is starting a new national network of science fiction book clubs The establishment and expansion of the network is as follows The original network began class=

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Using derivatives, it is found that the correct option is given by:

A. The expression 2x² + 20x + 32 represents the average rate of increase in the total number of clubs in the network across all states.

What is the meaning of the derivative of a function?

It is the rate of change of the function over a period of time.

In this problem, the total number of people in the book club after x months is given by:

f(x) = 2x³ + 20x² + 64x + 64

The derivative is given by:

f'(x) = 4x² + 40x + 64 = 2(2x² + 20x² + 32).

It represents the average rate of change across all states, hence option A is correct.

More can be learned about derivatives at https://brainly.com/question/2256078

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