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7nadin3 [17]
3 years ago
6

HELP PLZZZZZ 1.)Determine the first five terms of the sequence A(n) = A(n − 1) + 13, where A(1) = 21.

Mathematics
1 answer:
pishuonlain [190]3 years ago
8 0
Use math. Way it is very helpful
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What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i
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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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