Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula: t = ln 2 r Use the formula for Exercises 61–63. (See Example 8.) a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place. b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place. c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula: t = ln 2 r Use the formula for Exercises 61–63. (See Example 8.) a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place. b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place. c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
Solution Summary: The author calculates the time required by the investment to reach 6,000 if the interest rate is 5.5%.
Under continuous compounding, the amount of time t in years required for an investment to double is a function of the annual interest rate r according to the formula:
t
=
ln
2
r
Use the formula for Exercises 61–63. (See Example 8.)
a. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 5.5%? Round to one decimal place.
b. If you invest $3000, how long will it take the investment to reach $6000 if the interest rate is 8%? Round to one decimal place.
c. Using the doubling time found in part (b), how long would it take a $3000 investment to reach $12,000 if the interest rate is 8%?
Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045.
2) Find Θ given sec Θ = 4.213.
3) Find Θ given cot Θ = 0.579. Solve the following three right triangles.
B
21.0
34.6° ca
52.5
4)c
26°
5)
A
b
6) B 84.0 a
42°
b
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
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