where t is the number of years after 1950 and L(t) is given in billions of dollars. Evaluate and interpret the instantaneous rate of change in the total amount of consumer loans in the United States in 2020.
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- The annual revenue R (in millions of dollars) of OPet Foods since its inception can be modeled by R (t) = -0.0042 +4 +0.085 t3 -0.16 +2 -0.65 t + 3.4 where t is the t2 number of years since the store opened. In what year was the revenue first greater than $3.6 million? Round your answer to 1 decimal place. After Number years. Estimate from the graph of R(t) when OPet Foods had its lowest revenue over the first five years of existence. Round your answer to three decimal places. t= NumberUse the MU function derive from the TU function: TU = 200Q - 25Q^2 + Q^3 to draw a table up to the level of Q where MU is negative and graph the figuresSuppose that the world's current oil reserves is R = 2060 billion barrels. If, on average, the total reserves is decreasing by 15 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R= B.) 8 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)
- Find the calculations for 2018 and 2019, and enter the results in the following table.Year Quarter Revenue Q1 4.80 Q2 4.56 2015 Q3 4.88 Q4 4.91 Q1 5.37 Q2 4.99 2016 Q3 5.24 Q4 5.71 Q1 5.73 Q2 5.29 2017 Q3 5.66 Q4 5.70 Q1 6.07 Q2 6.03 2018 Q3 6.31 Q4 6.30 Q1 6.60 Q2 6.31 2019 Q3 6.82 Q4 6.75 Q1 7.10 Q2 6.00 2020 Q3 4.20 Q4 6.20An economist predicts that the cost of food will increase by 4% per year for the next several years. Part A: Use the economist's prediction to write an explicit rule for a geometric sequence that gives the cost in dollars of a box of cereal in year n that costs $3.20 in year 1. Part B: What is the fourth term of the sequence, and what does it represent in this situation? 5
- Explain why it is important that time-series variables are ‘stationary’. Outline a method that can be used to transform a non-stationary series into a stationary one.If the annual rate of world oil consumption t years after 1970 is modeledby the equation R(t) = 16.1e^.07t (billions of barrels per year), how much total oil (net change) was used between 1976 and 1980?The unemployment rate in a certain country was dropping at a constant rate of 0.2% (= 0.002, in decimals) between 2009 and 2019. In 2012, the unemployment rate was 3.5%.Let t be the number of years since 2009 and let U(t) be the unemployment rate at year t.(a) Find a formula for the function U. (Hint: use decimals in place of percentages.)U(t) =(b) Assuming the model is valid for a couple of more years after 2019, calculate the expected unemployment rate in year 2021. Enter your answer as a percentage.
- Please write all your steps regarding each calculation. Also, refer to the formula sheet; if any formula is used, please label it. Thankyou.Solve the following equation for x, where x represents a real number. X = 0.56x – 1.32 X = (Type an integer or a simplified fraction.)Economic time series are maintained and published by some government agencies such as the Census Bureau and the Bureau of Labor Statistics, and they use time series decomposition. Why do you think they use time series decomposition? Explain in detail.