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Nataliya [291]
2 years ago
8

Andrew researched the depreciation of cars and found that the value of the car he just bought halved every 5 years. Andrew purch

ased the car for $20,000 and he wants to find how many years it will take for the value of the car to reduce to $15,000. He wrote the equation 20000(5)^t/2=15000, and plans to solve for t. What change(s) should Andrew make to the equation to find the value of t in the above scenario? Use the half-life decay formula, m(t) = m o (1/2)^t/h, to answer the question.
A. t/2 should be replaced with 2t
B. 15000 and 20000 should be interchanged
C. 5 should be replaced with 1/2, and t/2 should be replaced with t/5
D. 5 should be replaced with 1/2, and t/2 should be replaced with 5t
Mathematics
1 answer:
natali 33 [55]2 years ago
8 0

Answer:

  C. 5 should be replaced with 1/2, and t/2 should be replaced with t/5

Step-by-step explanation:

The problem statement tells you the half-life of the car is 5 years. Using the value h = 5 in the given equation, you have ...

  m(t) = m₀(1/2)^(t/5)

The problem statement tells us the initial value of the car is $20,000, so we have ...

  m₀ = 20000

  m(t) = 20000(1/2)^(t/5)

Since Andrew wants the value of t when m(t) = 15000, his equation would read ...

  15000 =20000(1/2)^(t/5) . . . equation for finding when the value is 15000

__

The equation Andrew proposes to solve is ...

  20000(5)^(t/2) = 15000

In order to make his equation look like the the one above, the changes should be ...

  5 should be replaced with 1/2, and t/2 should be replaced with t/5.

_____

<em>Additional comment</em>

The equation can be solved as follows:

  15000/20000 = (1/2)^(t/5)

  log(3/4) = (t/5)log(1/2) . . . . take the log of both sides, simplify the fraction

  t = 5log(3/4)/log(1/2) . . . . divide by the coefficient of t

  t ≈ 2.08

Andrew's car will have a value of about $15,000 after 2 years and 1 month.

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Answer:

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Step-by-step explanation:

In general if we have a fraction ( mixed) as ,

a\dfrac{c}{d}

Then the improper fraction will be ,

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\dfrac{ d\times a + c}{d}

Using this concept we have ,

→ 125 ⅔

→ 125 × 3 + 2 / 3

→ 375 + 2/3

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<h3>Hence the simplified form of the expression is 377/3 .</h3>
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Answer:

x=  

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​  

 

​  

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Step-by-step explanation:

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BRAINLIEST <br> Solve for X. Round to the nearest tenth.
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Step-by-step explanation:

2 things to remember for problems like this :

the sum of all angles in a triangle is always 180 degrees.

the law of sines :

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so, now for the given problems :

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x/sin(90) = 12/sin(29)

x/1 = x = 12/sin(29) = 24.75198408...

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x/sin(74) = 37/sin(90) = 37

x = 37×sin(74) = 35.56668275...

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6.

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180 - 90 - 58 = 32 degrees.

x/sin(32) = 22/sin(58)

x = 22×sin(32)/sin(58) = 13.74712574...

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Determine the amount of money you would have if you invested $15,000 dollars for 11 years at 3% annual interest compounded conti
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Answer:

The amount after 3 years of investment is $20763  .

Step-by-step explanation:

Given as :

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Let The Amount after 3 years = $ A

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Amount = Principal × (1+\dfrac{\textrm rate}{100})^{\textrm time}

Or, A = p × (1+\dfrac{\textrm r}{100})^{\textrm t}

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