I suspect the given equation is incorrect because, as written, it is linear and that means the rate of change of volume is constant independent of price. Also there would be an increase in volume when the price increased, not a decrease because dy/dp would be positive. Please check.
a) If y=31(3p+1)^(-2/5)=31(3p+1)⁻⁰⋅⁴ then:
dy/dp=-12.4(3p+1)⁻¹⋅⁴×3=-37.2(3p+1)⁻¹⋅⁴.
When p=23, dy/dp=-0.097 (thousands of units per dollar).
b) This means that when p=$23, the volume is decreasing by 97 units per dollar increase of the price.
We can write dy=-0.097dp, as long as dp, the increase in price, is quite small, which means that if dp=$1 then dy=-0.097, a decrease of 97 units approximately.
Another approach is to avoid calculus and simple calculate y for p=$23 and p=$24. The difference in the y values gives the decrease in units. When we do this, the decrease is nearer to 94 units.