Due to ever-changing technology, a new xyz smartphone decreases in value 20% each year. (a) how much will this $1000 phone be worth in 2 years? (b) how long until it is worth less than 10% of it's original price?

10.3 years

Step-by-step explanation:

(a) Use the compound amount equation:  A = P(1 + rt), where, in this case,

P represents the original $1000 value and r is the rate of change.

Here, A = $1000(1 - 0.20)^2, or $1000(0.80)^2 = $640

the phone will be worth $640 after 2 years.

(b) "1/10 of its original price" would be (1/10)($1000) = $100.

Using the same equation:

$100 = $1000(0.80)^t

or:

1/10 = 0.80^t

Taking the natural log of both sides:

ln (1/10) = t ln 0.80, so that:

        -ln 10

t = = -2.3025 / (-0.2231)  =  10.3 years

       ln 0.80