Answer:
1. $640
2. About 10.3 years later
Step-by-step explanation:
This is a compound decay problem. The formula is
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>
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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.
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<em>Let's plug in and solve for t (we need to use logarithms):</em>
So, after 10.32 years, the phone would be worth less than 10% of original value.
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