8. Solve e 31 = 1000 for t. (Round to three decimal places as needed.) 9. Solve the equation. 55 p 2% = 110 If 55 @ 2k = 110, then k = (Type an exact answer.) 10. Find the general form of f if f'(x) = 4f(x). f(x) = 11. dA Find the general form of the function that satisfies - = - 9A. A(t) = 12. Between 2006 and 2016, the number of applications for patents, N, grew by about 4.6 per year. That is, N'(t) = 0.046N(t). Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 450,000 patent applications wer Estimate the number of patent applications in 2021. Estimate the rate of change in the number of patent applications in 2021. a) N(t) = b) The number of patent applications in 2021 will be (Round to the nearest whole number as needed.) c) The rate of change in the number of patent applications in 2021 is about (1) Round to the nearest whole number as needed.) (1) O year(s) per application. O application(s) per year. 13. In 2004, an art collector paid $118,574,000 for a particular painting. The same painting sold for $29,000 in 1950. Complete parts (a) through (d) a) Find the exponential growth rate k, to three decimal places, and determine the exponential growth function V, for which V(t) is the painting's v years after 1950. V(t) = Type an expression. Type integers or decimals for any numbers in the expression. Round to three decimal places as needed.) b) Predict the value of the painting in 2023. $ (Round to the nearest million as needed.) c) Estimate the rate of change of the painting's value in 2023. (1). Round to the nearest million as needed.) d) How long after 1950 will the value of the painting be $3 billion? year(s) (Do not round until the final answer. Then round to the nearest year as needed.) (1) O dollar(s) per year. O year(s) per dollar. 14. In 2011 a country's federal receipts (money taken in) totaled $2 25 trillion. In 2013, total federal receipts were $2.67 trillion. Assume that the gro receipts, F, can be modeled by an exponential function and use 2011 as the base year (t = 0). a) Find the growth rate k to six decimal places, and write the exponential function F(t), for total receipts in trillions of dollars. b) Estimate total federal receipts in 2015. c) When will total federal receipts be $12 trillion? a) Find the growth rate k. K= "Do not round until the final answer. Then round to six decimal places as needed.) Write the exponential function F(t)- F(t) = b) Estimate total federal receipts in 2015. The total federal receipts in 2015 will be approximately $ trillion. (Use the answer from part (a) to find this answer. Round to two decimal places as needed.) c) When will total federal receipts be $12 trillion? The total federal receipts will be $12 trillion approximately years after 2011. (Use the answer from part (a) to find this answer. Round to one decimal place as needed.)
