the price, in dollars per unit, that consumers are willing to pay for a popular high - end digital camera is…

the price, in dollars per unit, that consumers are willing to pay for a popular high - end digital camera is given by the accompanying function, where x is in thousands of units. complete parts (a) and (b). p(x)=1310 - 175 ln x\n\na) what price corresponds to a demand of 200,000 units?\nhow can the price that corresponds to a demand of 200,000 units be found? select the correct choice below and fill in the answer box to complete your choice. (simplify your answer.)\nevaluate p(200)\nsolve =1310 - 175 ln x for x\nthe price that corresponds to a demand of 200,000 units is $182.70 (round to the nearest cent as needed.)\nb) how many units will consumers buy at a price of $770 per camera?\nhow can the number of units that consumers will buy at a price of $770 per camera be found? select the correct choice below and fill in the answer box to complete your choice. (simplify your answer.)\na. solve =1310 - 175 ln x for x\nb. evaluate p()

the price, in dollars per unit, that consumers are willing to pay for a popular high - end digital camera is given by the accompanying function, where x is in thousands of units. complete parts (a) and (b). p(x)=1310 - 175 ln x\n\na) what price corresponds to a demand of 200,000 units?\nhow can the price that corresponds to a demand of 200,000 units be found? select the correct choice below and fill in the answer box to complete your choice. (simplify your answer.)\nevaluate p(200)\nsolve =1310 - 175 ln x for x\nthe price that corresponds to a demand of 200,000 units is $182.70 (round to the nearest cent as needed.)\nb) how many units will consumers buy at a price of $770 per camera?\nhow can the number of units that consumers will buy at a price of $770 per camera be found? select the correct choice below and fill in the answer box to complete your choice. (simplify your answer.)\na. solve =1310 - 175 ln x for x\nb. evaluate p()

Answer

Explanation:

Step1: Solve part a

Given $p(x)=1310 - 175\ln x$, and $x = 200$ (since $x$ is in thousands of units and 200000 units means $x = 200$). $p(200)=1310-175\ln(200)$ $\approx1310 - 175\times5.298317$ $=1310-927.205475$ $= 382.794525\approx382.79$

Step2: Solve part b

We are given $p(x) = 770$, so we set up the equation $770=1310 - 175\ln x$. First, rearrange the equation: $175\ln x=1310 - 770$ $175\ln x = 540$ $\ln x=\frac{540}{175}$ $x = e^{\frac{540}{175}}$ $x=e^{3.085714}\approx21.87$ (in thousands of units), so $x = 21870$ units.

Answer:

a) The price is $$382.79$. b) The number of units is $21870$.