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3 years ago

Money in a savings account is compounded continuously over time, t, and is modeled by the function

Mathematics

1 answer:

bezimeni [28]3 years ago

5 0

Answer:

1.7% compounded continuously

Step-by-step explanation:

The model used for continuous compounding is ...

f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have ...

f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

The balance grows at a continuous rate of 1.7%.

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Suppose there are two circles where the radius of one circle is twice the radius of the other circle. Each circle has an arc whe

Artemon [7]

Answer:

$L=2l$ where $l,L$ denote arc lengths of two circles

Step-by-step explanation:

Let $l,L$ denote arc lengths of two circles, $r,R$ denote corresponding radii and

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So,

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This implies $\alpha _1=\frac{l}{r}$ and $\alpha _2=\frac{L}{R}$

As each circle has an arc where the measures of the corresponding central angles are the same, $\alpha _1=\alpha _2$

$\frac{l}{r}=\frac{L}{R}$

As radius of one circle is twice the radius of the other circle,

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$\frac{l}{r}=\frac{L}{2r}\\\frac{l}{1} =\frac{L}{2}\\L=2l$

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