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Morgarella [4.7K]
2 years ago
10

Type the correct answer in the box. Round your answer to the hundredth.

Mathematics
1 answer:
sesenic [268]2 years ago
6 0

Answer:

Approximately 22.97 years

Step-by-step explanation:

Use the equation for continuously compounded interest, which uses the exponential base "e":

A=P e^{k*t}

Where P is the principal (initial amount of the deposit - unknown in our case)

A is the accrued value (value accumulated after interest is compounded), in our case it is not a given value but we know that it triples the original deposit (principal) so we write it as: 3 P (three times the principal)

k is the interest rate : 5% which translates into 0.05

and t is the time in the savings account to triple its value (what we need to find)

The formula becomes:

3P = P e^{0.05 * t}

To solve for "t" we divide both sides of the equation by P (notice it cancels P everywhere), and then to solve for the exponent "t" we use the natural logarithm function:

\frac{3P}{P} = \frac{P}{P}  e^{0.05 * t}

3 = e^{0.05 * t}

ln(3) = 0.05 * t

t = \frac{ln(3)}{0.05} = 21.972245... years

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Answer:

Second option, h=(x^{2} + 4x) ft

Step-by-step explanation:

Area = Base x Height

Height = Area ÷ Base

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3 years ago
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Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. Th
xenn [34]

Answer:

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Step-by-step explanation:

We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

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Thus replacing the functions of the exercise we get:

W = \left|\begin{array}{cc}e^{5x}&e^{2x}\\5e^{5x}&2e^{2x}\end{array}\right|

Working with the determinant we get

W = 2e^{7x}-5e^{7x}\\W=-3e^{7x}

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