The demand function for a certain product is determined by the fact that the product of the price and the quantity demanded equals 8000. The product currently sells for $3.40 per unit. Suppose manufacturing costs are increasing over time at a rate of 12% and the company plans to increase the price p at this rate as well. Find the rate of change of demand over time.

83.045( decreasing demand per unit time)

Step-by-step explanation:

let p be the price per product and q the number of units sold.

Given that p=$3.40 and q rate is 12%

-We are given that:

#We differentiate using product rule to get the rate at which demand changes over time:

Hence, demand is decreasing at a rate of 83.045 units per unit time.

ok then what happened.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)