Final answer:
The rate of change of supply price is found by differentiating the supply function, and then this derivative is evaluated at x = 31.5 to find the specific rate of change. To approximate the price increase from 31 to 32 units, multiply the rate by the change in units.
Step-by-step explanation:
The supply price's rate of change with respect to the number of units supplied from the given supply function P = 20 + 90ln(7x+8) can be found by differentiating the function with respect to x, which is dP/dx. For part (a), the derivative would give us the rate of change at any given number of units x. To find the rate of change of supply price when the number of units is 31.5 for part (b), we can simply plug x = 31.5 into the derivative of the supply price function and compute the value.
For part (c), to approximate the price increase when the number of units supplied changes from 31 to 32, we use the calculated rate of change at x = 31.5 and apply it to this small interval assuming the rate does not change much in this region.