49. Let f(t) be the temperature at time t where you live and suppose that at time t 3 you feel uncomfortably hot. How do you feel about the given data in each case? a. f (3) 2,f"(3) 4 Answer b. f (3) 2, f"(3)= -4 Answer c. f' (3)2, f" (3) 4 Answer d. f (3)2, f (3)4 Answer
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- The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N= 66 x−x2. Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,589. Round to the nearest integer. $The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?
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