Chapter 1.2, Problem 30EQ

Consider a forest where the population of a particular plant species grows exponentially. In a real-world scenario, we often deal with systems where the analytical function describing the phenomenon is not available. In such cases, numerical methods come in handy. For the sake of this task, however, you are provided with an analytical function so that you can compare the results of the numerical methods to some ground truth. The population P(t) of the plants at time t (in years) is given by the equation: P(t) = 200 0.03 t You are tasked with estimating the rate of change of the plant population at t = 5 years using numerical differentiation methods. First, compute the value of P'(t) at t = 5 analytically. Then, estimate P'(t) at t = 5 years using the following numerical differentiation methods: ⚫ forward difference method (2nd-order accurate) 3 ⚫ backward difference method (2nd-order accurate) ⚫ central difference method (2nd-order accurate) Use h = 0.5 as the step size and round all…

Nicole organized a new corporation. The corporation began business on April 1 of year 1. She made the following expenditures associated with getting the corporation started: Expense Date Amount Attorney fees for articles of incorporation February 10 $ 40,500 March 1-March 30 wages March 30 6,550 March 1-March 30 rent Stock issuance costs March 30 2,850 April 1-May 30 wages Note: Leave no answer blank. Enter zero if applicable. April 1 May 30 24,000 16,375 c. What amount can the corporation deduct as amortization expense for the organizational expenditures and for the start-up costs for year 1 [not including the amount determined in part (b)]? Note: Round intermediate calculations to 2 decimal places and final answer to the nearest whole dollar amount. Start-up costs amortized Organizational expenditures amortized

Last Chance Mine (LCM) purchased a coal deposit for $2,918,300. It estimated it would extract 18,950 tons of coal from the deposit. LCM mined the coal and sold it, reporting gross receipts of $1.24 million, $13 million, and $11 million for years 1 through 3, respectively. During years 1-3, LCM reported net income (loss) from the coal deposit activity in the amount of ($11,400), $550,000, and $502,500, respectively. In years 1-3, LCM extracted 19,950 tons of coal as follows: (1) Tons of Coal 18,950 Depletion (2) Basis (2)(1) Rate $2,918,300 $154.00 Tons Extracted per Year Year 1 4,500 Year 2 8,850 Year 3 6,600 Note: Leave no answer blank. Enter zero if applicable. Enter your answers in dollars and not in millions of dollars. a. What is LCM's cost depletion for years 1, 2, and 3? Cost Depletion Year 1 Year 2 Year 3