Dorothy Wagner is currently selling 80 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 2 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?

Increasing by $66 per day

Step-by-step explanation:

If sales are dropping at a rate of  2 per day, the sales function is:

If price is increasing by $1 per day, the daily price function is:

Revenue is given by daily sales multiplied by daily price:

The derivate of the revenue function gives us the daily rate of change in revenue:

Currently (t=0) her daily revenue is changing by:

Her revenue is increasing by $66 per day.

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