The table below shows the US unemployment rate during the Covid-19 pandemic. Let R = were jobless and seeking a job, with i in months since the beginning of 2020.¹ Jan Mar May Jul Sep 13.3 10.2 7.8 Month Unemployment rate (%) 3.5 4.4 www.bls.gov/charts/employment-situation/civilian-unemployment-rate.htm, accessed April 4, 2021. (a) When is f' (1) positive? Negative? Interpret in terms of unemployment. From the table we see that f' (t) is positive during When f' (1) is positive, unemployment is When f' (1) is negative, unemployment is + f (1) be the percent of US adults who and f' (t) is negative during (b) What is f (3)? Estimate f' (3) using the interval to the right. Give units. f(3) = i ƒ' (3) = i

The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. 2012 2014 2016 2018 2020 CO2 Emissions 338.5 364.5 397.1 423.8 452.1 498.4 Year 2010 Year 2022 2024 2026 2028 2030 CO2 Emissions 557.2 592.9 628.7 662.1 707.1 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.) y(x) = 2032 741.7 (b) Find the model's estimate for the 2024 data point. (Round your answer to two decimal places.) million metric tons Interpret the slope of the linear model. For each year since ---Select--- (c) Find the slope of the linear model. (Round your answer to two decimal places.) , carbon dioxide emissions in the U.S. are expected to change by million metric tons.

.A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.