answer and explain

Application of Derivative of Exponential and Logarithmic Functions Example 1: PriceDemand Model An Internet store sells Australian wool blankets. If the store sells x blankets at a price of lip per blanket. then the pricedemand equa tion is p = 3SEKO.999)'. Find the rate of change of price with respect to demand when the demand is 800 blankets and interpret the result. Example 2: Cable TV Subscribers A statistician used data from the US. Census Bureau to construct the model so) = 211m +2 where 50) is the number of cable TV subscribers (in millions) in year t (r = 0 corresponds to 1980). Use this model to estimate the number of cable TV sub scribers in 2015 and the rate of change of the number of subscribers in 2015. Round both to the nearest tenth of a million. Interpret these results Example 3: Salvage value. The estimated salvage value S (in dollars) of a company airplane after 1' years is given by 5(1) = 300.com 0.9)' What is the rate of depreciation (in dollars per year) after 1 year? 5 years? 10 years? Resale value. The estimated resale value R (in dollars) of a company car after 1' years is given by so) = 20.000( 0.86)' What is the rate of depreciation (in dollars per year) after 1 year? 2 years? 3 years? Example 5: Bacterial growth. A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. If we start with a colony of 5,000 bacteria, then after t hours. there will be AU) = 5,000 -2\" = 5,000 - 4' bacteria. Find A'(t), A'(l). and A'(S}, and interpret the results Example 6: Blood pressure. An experiment was set up to nd a rela- tionship between weight and systolic blood pressure in chil- dren. Using hospital records for 5,000 children, the experimenters found that the systolic blood pressure was given approximately by P(x) =17.5(1 + In x) 10 s x 5100 where P(x) is measured in millimeters of mercury and x is measured in pounds. What is the rate of change of blood pressure with respect to weight at the 40-ponnd weight level? At the 90-pound weight level? Example 7: Psychology: stimulus/response. In psychology, the Weber- Fechner law for the response to a stimulus is R = k In So where R is the response, S is the stimulus, and So is the low- est level of stimulus that can be detected. Find dR/dS. Example 8: Psychology: learning. A mathematical model for the aver- age of a group of people learning to type is given by N(t) = 10 + 6Int 121 where N(1) is the number of words per minute typed after t hours of instruction and practice (2 hours per day, 5 days per week). What is the rate of learning after 10 hours of in- struction and practice? After 100 hours