Answered

Get detailed and reliable answers to your questions on IDNLearn.com. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.

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

Sagot :

Sqdancefanidn

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.

_____

Additional comment

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.

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.