Superman comic book. In August 2014, a 1938 comic book featuring the first appearance of Superman sold at auction for a record price of $3.2 million. The comic book originally cost 10 ¢ ( $ 0.10 ) . ( Sources : eBay; money.cnn.com.) Use the two data points ( 0 , $ 0.10 ) and ( 76 , $ 3 , 200 , 000 ) , and assume that the value V of the comic book has grown exponentially, as given by d V d t = k V . (In the summer of 2010, a family faced foreclosure on their mortgage. As they were packing, they came across some old comic books in the basement, and one of them was a copy of this first Superman comic. They sold it and saved their house.) a. Find the function that satisfies this equation. Assume that V 0 = $ 0.10 b. Estimate the value of the comic book in 2020 c. What is the doubling time for the value of the comic book? d. After what time will the value of the comic book be $30 million, assuming there is no change in the growth rate?
Superman comic book. In August 2014, a 1938 comic book featuring the first appearance of Superman sold at auction for a record price of $3.2 million. The comic book originally cost 10 ¢ ( $ 0.10 ) . ( Sources : eBay; money.cnn.com.) Use the two data points ( 0 , $ 0.10 ) and ( 76 , $ 3 , 200 , 000 ) , and assume that the value V of the comic book has grown exponentially, as given by d V d t = k V . (In the summer of 2010, a family faced foreclosure on their mortgage. As they were packing, they came across some old comic books in the basement, and one of them was a copy of this first Superman comic. They sold it and saved their house.) a. Find the function that satisfies this equation. Assume that V 0 = $ 0.10 b. Estimate the value of the comic book in 2020 c. What is the doubling time for the value of the comic book? d. After what time will the value of the comic book be $30 million, assuming there is no change in the growth rate?
Superman comic book. In August 2014, a 1938 comic book featuring the first appearance of Superman sold at auction for a record price of $3.2 million. The comic book originally cost
10
¢
(
$
0.10
)
. (Sources: eBay; money.cnn.com.) Use the two data points
(
0
,
$
0.10
)
and
(
76
,
$
3
,
200
,
000
)
, and assume that the value V of the comic book has grown exponentially, as given by
d
V
d
t
=
k
V
.
(In the summer of 2010, a family faced foreclosure on their mortgage. As they were packing, they came across some old comic books in the basement, and one of them was a copy of this first Superman comic. They sold it and saved their house.)
a. Find the function that satisfies this equation. Assume that
V
0
=
$
0.10
b. Estimate the value of the comic book in 2020
c. What is the doubling time for the value of the comic book?
d. After what time will the value of the comic book be $30 million, assuming there is no change in the growth rate?
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
Could you explain this using the formula I attached and polar coorindates
Could you explain this using the formula I attached and polar coordinates
Chapter 3 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
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