4. The following table gives the profits of a concern for 5 years ending 2017 : Year 2013 2014 2015 2016 2017 Profitsur '000) 1.6 4.5 13.8 40.2 125.0 : Fit an equation of the type Ye= ab.
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- Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?As an active environmentalist who is interested in the impact of climate change on sea level, you focused in developing a mathematical model on the rise of sea level at Mount Kinabalu yearly. Assume that Mount Kinabalu is 4095m above sea level at the beginning of year 2015 as shown in Figure 2.0. However, due to climate change, you found out that there is an increment of 0.002% sea level at the end of each year. Let Pnrepresents the elevation of n years for Mount Kinabalu. Determine the linear recurrence relation after 1 year, 2 years and 3 years. Find a linear recurrence relation to describe the elevation after n What is the elevation of Mount Kinabalu at the end of year 2020?As an active environmentalist who is interested in the impact of climate change on sea level, you focused in developing a mathematical model on the rise of sea level at Mount Kinabalu yearly. Assume that Mount Kinabalu is 4095m above sea level at the beginning of year 2015 as shown in Figure 2.0. However, due to climate change, you found out that there is an increment of 0.002% sea level at the end of each year. Let Pnrepresents the elevation of n years for Mount Kinabalu. Determine the linear recurrence relation after 1 year, 2 years and 3 years. Find a linear recurrence relation to describe the elevation after n years. What is the elevation of Mount Kinabalu at the end of year 2020?
- Suppose that in a family savings equation, for the years 1990, 1991, and 1992, we let kidsit denote the number of children in family i for year t. If the number of kids is constant over this three-year period for most familiesin the sample, what problems might this cause for estimating the effect that the number of kids has on savings?2.) The manufacturer's suggested retail price (MSRP) for a particular car is $24,630, and it is expected to be worth $10,940 in 5 years. (a) Find a linear depreciation function for this car. (b) Estimate the value of the car 8 years from now. (c) At what rate is the car depreciating?Find the differential equation of the family of straight lines with slope 11
- Women in the Workforce The following table givesthe number of women age 16 years and older (inmillions) in the U.S. civilian workforce for selectedyears from 1950 and projected to 2050.a. Use x as the number of years past 1950 to create acubic model using these data.b. During what year does the model indicate that thenumber of women in the workforce will reach itsmaximum?The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a living organism, the ratio of radioactive carbon, carbon-14, to ordinary carbon stays fairly constant during the lifetime of the organism, being approximately equal to the ratio in the organism’s atmosphere at the time. After the organism’s death, however, no new carbon is ingested, and the proportion of carbon-14 in the organism’s remains decreases as the carbon-14 decays. Scientists who do carbon-14 dating often use a figure of 5730 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.Suppose that a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by f(t) = 10,000 − 900t (dollars per year). If money is worth 10%, compounded continuously, find the present value of the machine over the next 8 years.
- Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and continuously at a rate of $200 a year. Find the capital value at an interest rate of 5% compounded continuously.Suppose you deposit 3 000 at a 6% interest compounded continuously. What will the Average value of your account during the first 3 years be?Assume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration. Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?