Business-Depreciation. A farmer buys a new tractor for $157,000 and assumes that it will have a trade-in value of $82,000 after 10 years. The farmer uses a constant rate of depreciation (commonly called straight-line depreciation-one of several methods permitted by the IRS) to determine the annual value of the tractor. (A) Find a linear model for the depreciated value V of the tractor t years after it was purchased. (B) What is the depreciated value of the tractor after 6 years? (C) When will the depreciated value fall below $70,000? (D) Graph V for 0 ≤ t ≤ 20 and illustrate the answers from parts (B) and (C) on the graph.
Business-Depreciation. A farmer buys a new tractor for $157,000 and assumes that it will have a trade-in value of $82,000 after 10 years. The farmer uses a constant rate of depreciation (commonly called straight-line depreciation-one of several methods permitted by the IRS) to determine the annual value of the tractor. (A) Find a linear model for the depreciated value V of the tractor t years after it was purchased. (B) What is the depreciated value of the tractor after 6 years? (C) When will the depreciated value fall below $70,000? (D) Graph V for 0 ≤ t ≤ 20 and illustrate the answers from parts (B) and (C) on the graph.
Solution Summary: The author calculates the linear equation for the depreciated value V of the tractor, t years after it was purchased.
Business-Depreciation. A farmer buys a new tractor for
$157,000
and assumes that it will have a trade-in value of
$82,000
after 10 years. The farmer uses a constant rate of depreciation (commonly called straight-line depreciation-one of several methods permitted by the IRS) to determine the annual value of the tractor.
(A) Find a linear model for the depreciated value
V
of the tractor
t
years after it was
purchased.
(B) What is the depreciated value of the tractor after 6 years?
(C) When will the depreciated value fall below
$70,000?
(D) Graph
V
for
0
≤
t
≤
20
and illustrate the answers from parts (B) and (C) on the graph.
Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.
Taylor Series Approximation Example- H.W
More terms used implies better approximation
f(x) 4
f(x)
Zero order
f(x + 1) = f(x;)
First order
f(x; + 1) = f(x;) + f'(x;)h
1.0
Second order
0.5
True
f(x + 1) =
f(x) + f'(x)h +
ƒ"(x;)
h2
2!
f(x+1)
0
x; = 0
x+1 = 1
x
h
f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2
51
Taylor Series Approximation H.w:
Smaller step size implies smaller error
Errors
f(x) +
f(x,)
Zero order
f(x,+ 1) = f(x)
First order
1.0
0.5
Reduced step size
Second order
True
f(x + 1) = f(x) + f'(x)h
f(x; + 1) = f(x) + f'(x)h + "(xi) h2
f(x,+1)
O
x₁ = 0
x+1=1
Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5
iterations (or & s= 5%) for
f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2
52
Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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