
EBK LINEAR ALGEBRA: A MODERN INTRODUCTI
4th Edition
ISBN: 8220100476747
Author: POOLE
Publisher: Cengage Learning US
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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
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