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Alecsey [184]
3 years ago
14

Suppose that ​$17,183 is invested at an interest rate of 5.4​% per​ year, compounded continuously. ​a) Find the exponential func

tion that describes the amount in the account after time​ t, in years. ​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years? ​c) What is the doubling​ time?

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
8 0

Answer:

Total = Principal * e ^ (rate * years)

Total = 17,183 * 2.718281828459 ^ (.054 * years)

After 1 year = 18,136.39

After 2 years = 19,142.68

After 5 years = 22,509.12

After 10 years = 29,486.15

We'll use this formula to find the doubling time:

Years = ln (total / principal) / rate

we'll use 200 for total and 100 for principal

Years = ln (200 / 100) / rate

Years = ln (2) / .054

Years = 0.69314718056 / .054

Years = 12.8360588993  Years Doubling Time

Step-by-step explanation:

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Find the area that the curve encloses and then sketch it.<br> r = 3 + 8 sin(6)
Rudiy27

Answer:

A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2

Step-by-step explanation:

I assume you mean r=3+8\sin\theta:

Use the formula \displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta where a and b are the lower and upper bounds and r(\theta) is the equation of the polar curve.

Since the graph is symmetrical about the line \displaystyle \theta=\frac{\pi}{2}, let the bounds of integration be \displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr) to find half the area of the curve, and then find twice of that area:

\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta

\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\

A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

7 0
3 years ago
PLZZ HELP: A runner, training for a competition, ran on a track every day for 10 weeks. The first week he ran 8 kilometers each
Alekssandra [29.7K]

Answer:


Step-by-step explanation:

The values in column B were found by dividing both values in column A by 10. The values in column C were found by dividing both values in column B by 2. The other columns contain multiples of the values in column B.

If we look in column E, we can see that it would take her 45 minutes to run 6 miles.

If we look in column B, we can see that she could run 2 miles in 15 minutes.

If we look in column F, we can see that she is running 8 miles every 60 minutes (which is 1 hour), so she is running 8 miles per hour.

If we look in column C, we can see that her pace is 7.5 minutes per mile.

Solution: Finding a unit rate

If we divide 150 by 20, we get the unit rate for the ratio 150 minutes for every 20 miles.

150÷20=7.5

So the runner is running 7.5 minutes per mile. We can multiply this unit rate by the number of miles:

7.5minutesmile×6 miles=45 minutes

Thus it will take her 45 minutes to run 6 miles at this pace.

If it takes her 45 minutes to run 6 miles, it will take her 45÷3=15 minutes to run 6÷3=2 miles at the same pace.

If it takes her 15 minutes to run 2 miles, it will take her 4×15=60 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.

We found her pace in minutes per miles in part (a).

hope it helps


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Three is the answer, pretty sure
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Three friends each have a balance of $5,000 on their credit cards with a 25% APR. They've decided that they will not make any ot
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Answer:

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A square pyramid has a slant height of 15 cm. A side length of the base is 20 cm. What is the surface area of the pyramid? Enter
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Answer:

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Step-by-step explanation:

Pretty sure

4 0
3 years ago
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