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Nimfa-mama [501]
3 years ago
6

A deposit of $200 is made in an account at the beginning of each month at an annual interest rate of 3% compounded monthly. The

balance in the account after n months is An = 200(401)(1.0025n ? 1).(Round your answers to two decimal places.)
(a) Compute the first six terms of the sequence {An}.
A1 = $
A2 = $
A3 = $
A4 = $
A5 = $
A6 = $
(b) Find the balance in the account after 5 years by computing the 60th term of the sequence.
A60 =
(c) Find the balance in the account after 15 years by computing the 180th term of the sequence.
A180 =
Mathematics
1 answer:
Step2247 [10]3 years ago
8 0

Complete questions:

A deposit of $200 is made in an account at the beginning of each month at an annual interest rate of 3% compounded monthly. The balance in the account after n months is An = 200(401)(1.0025^n - 1).(Round your answers to two decimal places.)

Answer:

Kindly check explanation

Step-by-step explanation:

Given the amount of balance in an account after. 'n' months using the eqation:

An = 200(401)(1.0025^n - 1)

(a) Compute the first six terms of the sequence {An}.

A1 = 200(401)(0.0025) = $200.50

A2 = 200(401)(1.0025^2 - 1) = $401.50

A3 = 200(401)(1.0025^3 - 1) = $603.00

A4 = 200(401)(1.0025^4 - 1) = $805.01

A5 = 200(401)(1.0025^5 - 1) = $1007.53

A6 = 200(401)(1.0025^6 - 1) = $10210.54

B) balance 5 years after n = 5 * 12 = 60

A60 = 200(401)(1.0025^60 - 1) = $12,961.67

C.) balance 15 years after ; n = 15 * 12 = 180

A180 = 200(401)(1.0025^180 - 1) = $45,508.02

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The height of the <em>water</em> depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.

<h3>How to derive equations for periodical changes in time</h3>

According to the two cases described in the statement, we have clear example of <em>sinusoidal</em> model for the height as a function of time. In this case, we can make use of the following equation:

h = a + A · sin (2π · t/T + B)     (1)

Where:

  • a - Initial position, in meters.
  • A - Amplitude, in meters.
  • t - Time, in hours or seconds.
  • T - Period, in hours or seconds.
  • B - Phase, in radians.

Now we proceed to derive the equations for each case:

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A = (20 m - 8 m)/2

A = 6 m

a = 14 m

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20 = 14 + 6 · sin B

6 = 6 · sin B

sin B = 1

B = π/2

h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.

Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):

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A = 19 m

a = 21 m

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2 = 21 + 19 · sin B

- 19 = 19 · sin B

sin B = - 1

B = - π/2

h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.

Lastly, we proceed to graph each case in the figures attached below.

To learn more on sinusoidal models: brainly.com/question/12060967

#SPJ1

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