anonymous
  • anonymous
The value V(t) of a $18,000 car after t years that depreciates at 20% per year is given by the formula V(t) = V0(b)t. What is the value of V0 and b, and what is the car's value after 5 years (rounded to the nearest cent)? Hint: Use the equation b = 1 − r to determine depreciation. V0 = $18,000, b = 0.80, and the value after 5 years is $5,898.24 V0 = $18,000, b = 0.20, and the value after 5 years is $5.76 V0 = $18,000, b = 1.20, and the value after 5 years is $44,789.76 V0 = $18,000, b = 0.80, and the value after 5 years is $5,760.00
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@GreenCat are you able to help me with this?
GreenCat
  • GreenCat
no sorry
phi
  • phi
Hint: Use the equation b = 1 − r that is not much of a hint, unless you know what "r" is supposed to be. Do you know what they mean by r ?

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anonymous
  • anonymous
It means doubling or 2 in this case. @phi
phi
  • phi
it can't mean that. they say depreciates at 20% per year depreciate means "go down in value" I guess they mean r is 0.2 (20% written as a decimal) so "b" in your formula , using the hint is 1-0.2
anonymous
  • anonymous
Ok that makes sense. This lesson has been really hard for me to understand. Is there anyway that you might be able to talk me through this question? @phi
phi
  • phi
If you have time
anonymous
  • anonymous
Yes I do. I'm pretty sure that it's either a or d. Because b= 1-0.2 = 0.8
phi
  • phi
yes.
phi
  • phi
First step Do you know what 10% of 100 is ? i.e. do you know how to find 10% of 100 ?
anonymous
  • anonymous
It would be 10/100, which is 10
phi
  • phi
you would write 10% as 10/100 (which simplifies to 0.1 as a decimal) then you do 0.1 * 100 you get 10 can you do 10% of 50 ?
anonymous
  • anonymous
It's 5
phi
  • phi
yes. But I want to make sure you get the idea say you want 1/2 of 20 you would multiply 1/2 * 20 and get 10 or 1/3 of 90 you would multiply 1/3* 90 and get 30 does that make sense?
phi
  • phi
percents are the same idea, except the fraction always has 100 in the bottom 20% is the fraction 20/100 and 20% of 100 you do by multiplying the fraction 20/100 * 100 you would get 20
anonymous
  • anonymous
Yes that makes sense. I'm following you
phi
  • phi
That is the first idea that you have to be comfortable with. Now the second idea 100 is reduced by 10% that is short-hand (i.e. they leave some words out) for 100 is reduced by 10% of 100 and that means 100 minus 10% of 100 or in math 100 - 0.1*100 do you know what that is ?
anonymous
  • anonymous
Would that be 9990?
phi
  • phi
first what is 0.1*100 ?
anonymous
  • anonymous
It's 99.9
phi
  • phi
you calculator is broken what is \[ \frac{100}{10} \]
anonymous
  • anonymous
I'm sorry I do not know how I got that. It's 10. 0.1*100 = 10
phi
  • phi
yes. If you are not good with arithmetic, make a note to study it more. (Khan has lots of videos ) In the meantime, you can survive using a calculator
phi
  • phi
back to the 2nd idea something costs $20 then they say, "on sale! 10% off" when they say 10% off they mean 1) find 10% of 20 can you do that ?
anonymous
  • anonymous
10/100 *20 =2
phi
  • phi
yes, something costs $20 then they say, "on sale! 10% off" when they say 10% off they mean 1) find 10% of 20, which is 2 2) take 2 off of 20, i.e. figure out 20 -2
phi
  • phi
in other words, the new price will be $18 ok so far?
phi
  • phi
the next idea is is to write 10% off as \[ 20- \frac{10}{100} 20 = 20\left(1-\frac{10}{100} \right) \] that uses the "distributive property" 1 - 0.1 = 0.9
phi
  • phi
in other words, 10% of 20 can be written as 20 - 20*0.1 = 20(1-0.1) = 20*0.9 if you multiply 20*0.9 you get 18 (the same answer as before)
anonymous
  • anonymous
Yes! My computer messed up for a sec. I think I actually figured out the answer. If you do the equation this way. 18,000(0.80)^5 you get 147,456/25. And if you simplify that, you get 5898.24. And that is choice A!!!
anonymous
  • anonymous
Is that right?
phi
  • phi
I'm not sure how you got 147456/25, but yes that is the correct answer on my calculator I would do 0.8^5 and get 0.32768 then multiply by 18000
anonymous
  • anonymous
I have a few more that I need help with. Do you have time to help me?
phi
  • phi
one more
anonymous
  • anonymous
The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 8.6 days and there is an amount equal to 15 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 37 days? Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life. A(t) = 15(0.5)8.6t, 0.0 gram remaining A(t) = 15(0.5)t/8.6, 0.8 gram remaining A(t) = 8.6(15)(0.5)t, 0.0 gram remaining A(t) = 15(0.5)8.6/t, 12.8 grams remaining
phi
  • phi
Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life to use their formula you have to interpret the info they gave you. For example, you need to know A0 , which is the "initial amount" any idea what the initial amount is ?
anonymous
  • anonymous
I think that it is 15. Is that right?
phi
  • phi
yes. they say there is an amount equal to 15 grams now. so you start with 15 grams (initial means starting or first. Like initial is the first letter of your name)
phi
  • phi
so put in 15 into the equation \[ A(t) = A0(0.5)^{\frac{t}{H}} \\ A(t) = 15(0.5)^{\frac{t}{H}} \]
phi
  • phi
you also need H is the half-life what is H ?
anonymous
  • anonymous
the half life would be 8.6?
phi
  • phi
so we put that in \[ A(t) = 15(0.5)^{\frac{t}{8.6}} \]
anonymous
  • anonymous
then 37 would be t?
phi
  • phi
they say "t" is time (starting from now) in days so put in 37 for t \[ A(t) = 15(0.5)^{\frac{37}{8.6}} \]
phi
  • phi
I guess I should write A(37) =
anonymous
  • anonymous
I got 0.7602601167 and then when I round to the nearest tenth it would be 0.8. Right?
phi
  • phi
yes. But only one of the choices has the correct formula, so we did not need to find the actual number
anonymous
  • anonymous
So the correct answer would be B?
phi
  • phi
yes
anonymous
  • anonymous
Thank you so much! It makes so much more sense! I really appreciate it. I only have one more question now. You really helped me :) Thank you

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