Question

The value of a home theater system depreciates by about 7% each year. Aeryn purchases s home theater system for 3000. What is its value after 4 years? Round your answer to the nearest hundred

Answer 1

The value after 4 years is $ 2244.16

Solution:

The decreasing function is given as:

$y = a(1-r)^t$

Where,

y is final value

a is initial value

r is decreasing rate in decimal

t is number of years

From given,

a = 3000

t = 4 years

$r = 7 \% = \frac{7}{100} = 0.07$

Substituting the values we get,

$y = 3000(1-0.07)^4\\\\y = 3000 \times 0.93^4\\\\y = 3000 \times 0.74805201\\\\y = 2244.15603\\\\y \approx 2244.16$

Thus the value after 4 years is $ 2244.16