The daily sales of t-shirts can be represented by the linear demand equation \( q=590-4 p \). Find the price elasticity of demand when the price is \( \$ 45 \) per \( t \)-shirt. (Round your answer to 2 decimal places.)

To find the price elasticity of demand, we need to use the formula for price elasticity of demand, which is given by: \[ E_d = \frac{dq/dp \cdot p}{q} \] First, we have the demand equation: \[ q = 590 - 4p \] To calculate \( dq/dp \), we differentiate \( q \) with respect to \( p \): \[ \frac{dq}{dp} = -4 \] Next, we need to find \( q \) when \( p = 45 \): \[ q = 590 - 4(45) = 590 - 180 = 410 \] Now we can plug in the values into the elasticity formula: \[ E_d = \frac{-4 \cdot 45}{410} = \frac{-180}{410} \approx -0.439 \] Rounding to two decimal places, the price elasticity of demand when the price is \( \$45 \) per t-shirt is approximately \( -0.44 \).