Final answer:
The rate of change of demand with respect to the price is -240p² T-shirts per unit change in price.
Step-by-step explanation:
The demand for the bie-dyed T-shirts is given by the formula σ = 490 - 80p³, where σ represents the demand in T-shirts per month and p represents the price per T-shirt.
To find the rate of change of demand with respect to the price (dt/dθ), you need to differentiate the demand function with respect to p.
Differentiating the function σ = 490 - 80p³, we get dt/dθ = -240p².
Therefore, the rate of change of demand with respect to the price is -240p² T-shirts per unit change in price.