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Reil [10]
4 years ago
11

how long does it take for an investment to double in value if it is invested at 8% per annum compounded monthly? compounded cont

inuously?
Mathematics
1 answer:
ella [17]4 years ago
7 0
2p=p(1+0.08/12)^12n
2=(1+0.08/12)^12n
Log(2)=12n*log(1+0.08/12)
12n=log(2)/log(1+0.08/12)
n=104.32/12
N=8.7 years
Continuously
2p=pe^rt
Now your turn solve with math to get the answer using the equation...if you have problem with that just tell me
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Step-by-step explanation:

\underline{ \underline{ \text{Given}}}  :

  • \tt{ {A}^{T}  = \begin{bmatrix} 2 &  - 4 \\ 4 & 3 \\ \end{bmatrix}}

\underline{ \underline { \text{To \: Find}}} :

  • \sf{ {A}^{2}  - 5A+ 22I= 0}

\underline{ \underline{ \text{Solution}}} :

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by \sf{ {A}^{T}}. Again , Interchange it's rows and columns in order to find ' A '.

\tt{A = \begin{bmatrix} 2 &  4 \\  - 4 & 3 \\ \end{bmatrix}}

Now , LEFT HAND SIDE ( L.H.S )

\tt{ {A}^{2}  - 5A+ 22I}

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ \begin{bmatrix} 2 &   4 \\  - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 &  4 \\ -  4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 &   4 \\  - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 &   0 \\  0 & 1\\ \end{bmatrix}

⟼ \begin{bmatrix} 2  \times 2 + 4 \times ( - 4)&   2  \times 4 + 4 \times 3 \\  - 4 \times 2 + 3 \times ( - 4) &  - 4  \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 &   20 \\   - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 &   0 \\  0 & 22 \\ \end{bmatrix}

⟼ \begin{bmatrix} 4 + ( - 16) &   8 + 12 \\   - 8 + ( - 12) &  - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 &   20 \\   - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 &   0 \\  0 & 22 \\ \end{bmatrix}

⟼ \begin{bmatrix} - 12 &   20\\  - 20&  - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 &   20 \\   - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 &   0 \\  0 & 22 \\ \end{bmatrix}

⟼ \begin{bmatrix}  - 22 &   0 \\  0&  - 22 \\ \end{bmatrix}  + \begin{bmatrix} 22 &   0 \\  0 & 22 \\ \end{bmatrix}

⟼ \begin{bmatrix}  - 22 + 22 &   0 + 0 \\  0 + 0 &  - 22  + 22 \\ \end{bmatrix}

⟼ \begin{bmatrix} 0 &   0\\  0 & 0 \\ \end{bmatrix}

⟼ \sf{0}

RIGHT HAND SIDE ( R.H.S ) : 0

L.H.S = R.H.S [ Hence , proved ! ]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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4 0
3 years ago
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