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Montano1993 [528]
4 years ago
14

Suppose your friend's parents invest $25,000 in an account paying 5% compounded anually. What will be the balance be after 9 yea

rs?
Mathematics
2 answers:
sergey [27]4 years ago
7 0

Answer:

The balance of your friend's parents account will be $38,783.21 cents after 9 years.

Step-by-step explanation:

Year 1: 25,000(1.05)

Year 1: $26,250

Year 2: 26,250(1.05)

Year 2: $27,562.5

Year 3: 27,562.5(1.05)

Year 3: $28,940.625

Year 4: 28,940.625(1.05)

Year 4: $30,387.6563

Year 5: 30,387.6563(1.05)

Year 5: $31,907.0391

Year 6: 31,907.0391(1.05)

Year 6: $33,502.3911

Year 7: 33,502.3911(1.05)

Year 7: $35,177.5107

Year 8: 35,177.5107(1.05)

Year 8: $36,936.3862

Year 9: 36,936.3862(1.05)

Year 9: $38,783.2055

Mamont248 [21]4 years ago
4 0
<h2>Answer:</h2>

$38 783.2

<h2>Step-by-step explanation:</h2>

The equation is:

25 000*1.05^{9}

(1.05 because 5% is 0.05 of the whole)

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The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy
vesna_86 [32]

Answer:

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

Step-by-step explanation:

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.

This means that the consumption after t years is given by the following differential equation:

\frac{dC}{dt} = kC

In which k is the growth rate.

The solution is, applying separation of variables:

C(t) = C(0)e^{kt}

In which C(0) is the initial consumption.

The town consumed 4.4 trillion British thermal units (BTUs) initially.

This means that C(0) = 4.4

So

C(t) = C(0)e^{kt}

C(t) = 4.4e^{kt}

5.5 trillion BTUs annually after 5 years.

This means that C(5) = 5.5. We use this to find k. So

C(t) = 4.4e^{kt}

5.5 = 4.4e^{5k}

e^{5k} = \frac{5.5}{4.4}

e^{5k} = 1.25

\ln{e^{5k}} = \ln{1.25}

5k = \ln{1.25}

k = \frac{\ln{1.25}}{5}

k = 0.0446

So

C(t) = 4.4e^{0.0446t}

After 9 years?

This is C(9). So

C(9) = 4.4e^{0.0446*9} = 6.57

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

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3 years ago
Find a positive angle less than 360° that is coterminal with the given angle.
Naddik [55]

Answer:

The positive angle less than 360° that is coterminal with -215° has a measure of 145°.

Step-by-step explanation:

From Geometry, we know that angles form a family of coterminal angles as function of number of revolutions done on original angle. We can represent the set of all coterminal angles by means of the following expression:

\theta_{c} = \theta_{o} + 360\cdot i, i \in \mathbb{Z} (1)

Where:

\theta_{o} - Original angle, in sexagesimal degrees.

\theta_{c} - Coterminal angle, in sexagesimal degrees.

i - Coterminal angle index, no unit.

If we know that \theta_{o} = -215^{\circ} and i = 1, then the coterminal angle that is less than 360° is:

\theta_{c} = -215^{\circ} + 360\cdot (1)

\theta_{c} = 145^{\circ}

The positive angle less than 360° that is coterminal with -215° has a measure of 145°.

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Answer:

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