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Vlada [557]
2 years ago
8

The population of a town is 18,000.

Mathematics
1 answer:
Eddi Din [679]2 years ago
7 0
If the town decreases at a rate of 8% per year, it would take 6 years.

100% - 8% = 92%

We would multiply each population per year by 0.92 as the town is decreasing in population by 8% per year

1st year: 18,000 • .92 = 16,560

2nd year: 16,560 • .92 = 15,235.2

3rd year: 15,235.2 • .92 = 14,016.384

4th year: 14,016.384 • .92 = 12,894.72

5th year: 12,894.72 • .92 = 11,863.1424

6th year: 11,863.1424 • .92 = 10,914.091

10,914 is less than 11,000 meaning it would take 6 years for the population to be fewer than 11,000 if the town is decreasing in population at a rate of 8% per year

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Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to
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Answer:

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

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And then the value of t would be:

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And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

A =P e^{rt}

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means A= 300000 and we want to find the value for t.

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

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And rounded to the nearest tenth would be 9.2 years.

5 0
3 years ago
Solve each system by substitution.<br> 5) 5x + 3y =-23<br> y = 4
docker41 [41]

Answer:

(- 7, 4 )

Step-by-step explanation:

Given the 2 equations

5x + 3y = - 23 → (1)

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Substitute y = 4 directly into (1_

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5x = - 35 ( divide both sides by 5 )

x = - 7

Solution is (- 7, 4 )

3 0
3 years ago
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