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Sergeeva-Olga [200]
2 years ago
15

The Johnson family want to start a college fund for their daughter Gabriella. They put $63, 000 in to an account that grows at a

rate of 2.55% per year, compounded quaterly. Given the function G(t)= 63,000(1+ .0255/4)^ 4t, where G(t) represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account.
Calculate the number of years it will take for the account to reach approximately $150,000, to the nearest hundredth of a year.
Mathematics
1 answer:
marissa [1.9K]2 years ago
6 0

Answer:

  • 34.13 years

Step-by-step explanation:

<u>Given formula:</u>

  • G(t)= 63000(1 + 0.0255/4)^4t

<u>Need to find the value of t when G(t) = 150000</u>

  • 150000 = 63000( 1+ 0.0255/4)^4t
  • ( 1+ 0.0255/4)^4t = 150000/63000
  • ( 1+ 0.0255/4)^4t = 2.3809
  • 4t* log( 1+ 0.0255/4) = log 2.3809
  • 4t *0.00275983965 = 0.37674115501
  • t = 0.37674115501/(4*0.00275983965)
  • t = 34.13 years rounded

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The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

<h3>How can the distance between Vic and Dan be calculated?</h3>

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Dan's distance  =  \frac{553.3}{tan ( {72}^{ \circ} )}  = 179.8

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Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan <em>d </em>is found as follows;

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Learn more about Pythagorean theorem here:

brainly.com/question/343682

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