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ExtremeBDS [4]
3 years ago
12

What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i

ncrease 150% in 5 years?
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
5 0

Answer:

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

Step-by-step explanation:

Use the formula for continuous compounding

X(t) = Pe^{rt}

where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.

(this formula can be beautifully derived from just basic considerations, btw)

We are given t=5, and percent increase on the initial P, so we can solve for r

X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

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A regulation basketball has a diameter of about 9 in. What is the best approximation for the volume of this ball? 3050 in³ 382 i
Mandarinka [93]

The best apporximation for the volume of this ball is 382 cubic inches.

<h3>What is the volume of the ball?</h3>

The volume of the ball is calculated by the formula V = 4 / 3πr³. This formula is the same in the whole world.

Given

A regulation basketball has a diameter of about 9 in.

The radius of the ball is;

\rm Radius = \dfrac{Diameter}{2}\\\\Radius=\dfrac{9}{2}\\\\Radius=4.5\ inches

The volume of the ball is;

\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume=\dfrac{4}{3} \times 3.14 \times 4.5^3\\\\Volume =\dfrac{144.53}{3}\\\\Volume = 381.51\\\\Volume = 382 \ In^3 \ apporx

Hence, the best apporximation for the volume of this ball is 382 cubic inches.

To know more about volume click the link given below.

brainly.com/question/10647788

4 0
2 years ago
11 divided by 0.1595
schepotkina [342]

Answer:

68.965

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
5.3.24 A is a 3times3 matrix with two eigenvalues. Each eigenspace is​ one-dimensional. Is A​ diagonalizable? Why? Select the co
abruzzese [7]

Answer:

C. No. The sum of the dimensions of the eigenspaces equals nothing and the matrix has 3 columns. The sum of the dimensions of the eigenspace and the number of columns must be equal.

Step-by-step explanation:

Here the sum of dimensions of eigenspace is not equal to the number of columns, so therefore A is not diagonalizable.

5 0
3 years ago
Please help with one question
Genrish500 [490]
I think your answer would be C.
8 0
3 years ago
Pls help and give steps pls I give brainliest thank uuuu
krek1111 [17]

Answer: 42 cm to the power of 3

Step-by-step explanation: L x w x h

3 x 7 x 2

21 x 2

42

6 0
3 years ago
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