Answer:
1. $640
2. About 10.3 years later
Step-by-step explanation:
This is a compound decay problem. The formula is
![F=P(1-r)^t](https://tex.z-dn.net/?f=F%3DP%281-r%29%5Et)
Where
F is the future amount
P is the initial amount
r is the rate of decrease (in decimal), and
t is the time in years
<u>Question 1:</u>
We want to find F after 2 years of a phone initially costing 1000. So,
P = 1000
r = 20% or 0.2
t = 2
<em>plugging into the formula, we solve for F:</em>
<em>
</em>
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The phone is worth $640 after 2 years
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<u>Question 2:</u>
We want to find when will the phone be worth 10% of original.
10% of 1000 is 0.1 * 1000 = 100
So, we want to figure this out for future value of 100, so F = 100
We know, P = 1000 r = 0.2 and t is unknown.
<em />
<em>Let's plug in and solve for t (we need to use logarithms):</em>
![F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32](https://tex.z-dn.net/?f=F%3DP%281-r%29%5Et%5C%5C100%3D1000%281-0.2%29%5Et%5C%5C100%3D1000%280.8%29%5Et%5C%5C%5Cfrac%7B100%7D%7B1000%7D%3D0.8%5Et%5C%5C0.1%3D0.8%5Et%5C%5Cln%280.1%29%3Dln%280.8%5Et%29%5C%5Cln%280.1%29%3Dt%2Aln%280.8%29%5C%5Ct%3D%5Cfrac%7Bln%280.1%29%7D%7Bln%280.8%29%7D%5C%5Ct%3D10.32)
So, after 10.32 years, the phone would be worth less than 10% of original value.
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