The U.S. Energy Information Administration projected that imports of petroleum products in 2005 would be 4.81 quadrillion Btu and would increase by 5.47% each year through 2020.T (a) Find the function of the model that gives projected petroleum imports in quadrillion Btu, where t is the number of years since 2005, with data from 0 sts 15 P(t) = quadrillion Btu (b) According to the model, when will imports exceed 7 quadrillion Btu? (Round your answer for t to two decimal places.) Imports will exceed 7 quadrillion Btu in t= years which will occur in the year (c) Describe the end behavior of the model as time increases. P(t) increases without bound as t increases. O P(t) approaches a limiting value of 33.67 as t increases. OP(t) decreases without bound as t increases P(t) remains constant as t increases. OP(t) decreases toward 0 as t increases

Each month, Uncle Joe’s Auto Parts uses exponential smoothing (with α = 0.25) to predict the number of barrels of brake fluid that will be sold during the next month. In June Uncle Joe forecast that he would sell 37 barrels of brake fluid during July. Uncle Joe actually sold 43barrels in July. What is Uncle Joe’s forecast for brake fluid sales in August and September?

We have a large tank filled with 50 liters of pure water. there is a salt solution of concentration 20 g/L flowing into the tank at a rate of 2 L/min. The well mixed solution is flowing out of the tank at a rate of 1 L/min. find the concentration  of salt in the tank as a function of time. no need to worry about the tank overflowing.

According to the U.S. Census Bureau, in 2011, the median (middle of the range) annual income of a high school graduate with no further education was about $35,400 per year. If we assume that it takes 4 years to earn a bachelor's degree and 2 additional years to earn a master's degree, the median annual income increases by 12% for each year spent toward successful completion of a degree. This describes a function  I = I(y),  where I is the median income in 2011 for a person with y years of college education. (a) Express in functional notation the median income in 2011 of an individual with a bachelor's degree, which requires 4 years of college. Calculate the value. (Round your answer to the nearest cent.) I         = $  (b) Make a table of values that shows the median income in 2011 for individuals completing 0 through 4 years of college. (Round your answers to the nearest cent.) Years of college Median income (in 2011) 0 $  1 $  2 $  3 $  4 $  (c) Make a…

Imagine that COVID-19 had spread exponentially in Maine since the first case (on March 12). Using the model f(t)=A02t/d  with A0=1 and t= number of days since March 12, find D with the knowledge that there were 7,603 total cases on Nov. 7, 240 days after March 12.

A client’s orders are growing consistently at x% per year.     A) If three years from now orders are 50% higher than today, what is the annual growth rate (x)?     B) Write an expression (in terms of x) for how many years it will take until orders are double what they are currently