A farmer depreciates a $120,000 tractor. He estimates that the resale value V t in $1000 of the tractor t years after purchase is 80 % of its value from the previous year. Therefore, the resale value can be approximated by V t = 120 0.8 t . a. Find the resale value 5 yr after purchase. Round to the nearest $1000 . b. The farmer estimates that the cost to run the tractor is $ 18 / hr in labor, $36 / hr in fuel, and $22 / hr in overhead colts (for maintenance and repair). Estimate the farmer's cost to run the tractor for the first year if he runs the tractor for a total of 800 hr. Include hourly costs and depreciation.
A farmer depreciates a $120,000 tractor. He estimates that the resale value V t in $1000 of the tractor t years after purchase is 80 % of its value from the previous year. Therefore, the resale value can be approximated by V t = 120 0.8 t . a. Find the resale value 5 yr after purchase. Round to the nearest $1000 . b. The farmer estimates that the cost to run the tractor is $ 18 / hr in labor, $36 / hr in fuel, and $22 / hr in overhead colts (for maintenance and repair). Estimate the farmer's cost to run the tractor for the first year if he runs the tractor for a total of 800 hr. Include hourly costs and depreciation.
A farmer depreciates a
$120,000
tractor. He estimates that the resale value
V
t
in $1000
of the tractor t years after purchase is
80
%
of its value from the previous year. Therefore, the resale value can be approximated by
V
t
=
120
0.8
t
.
a. Find the resale value 5 yr after purchase. Round to the nearest
$1000
.
b. The farmer estimates that the cost to run the tractor is
$
18
/
hr
in labor,
$36
/
hr
in fuel, and
$22
/
hr
in overhead colts (for maintenance and repair). Estimate the farmer's cost to run the tractor for the first year if he runs the tractor for a total of 800 hr. Include hourly costs and depreciation.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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