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mina [271]
2 years ago
5

If line PQ and line RS are different names for the same line, what must be true about points P, Q, R, and S?

Mathematics
1 answer:
Law Incorporation [45]2 years ago
8 0

Answer:

They are collinear

Step-by-step explanation:

They are all on the same line.

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your
bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

D = \frac{72}{Interest Rate}

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In our exercise, the interest rate is 7.7%. So, by the rule of 72:

D = \frac{72}{7.7} = 9.35.

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

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A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

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We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

A = 2P

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There are 52 weeks in a year, so n = 52

A = P(1 + \frac{r}{n})^{nt}

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2 = (1.0015)^{52t}

Now, we apply the following log propriety:

\log_{a} a^{n} = n

So:

\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2

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t = \frac{462.44}{52}

t = 8.89

The exact answer is that the doubling time is 8.89 years.

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