Question

jimmy bought an X-BOX ONE for 700$. The value of the gaming console decreases 12% each year. About how long will it take for the value of the television to be reduced to 200$.

Answer 1

600 jfjfjrrkekejrjjfkfkd

Answer 2

Answer:

9.8 years

Step-by-step explanation:

To solve this we need to isolate "t" variable in the following equation:

$A_{final}=A_{initial}(1+r)^{t}$

Where the final amount is $200, initial amount is $700 (really xbox 1 was like $300 on release day but okaayyy), and the rate is 12% which is 0.12 in decimals (12%÷100=0.12).   By plugging in those values we obtain:

$200=700(1-0.12)^t\\\\200=700(0.88)^t$

To solve for t we must use logarithms and so:

$200=700(0.88)^t\\\\\frac{200}{700}=0.88^t\\\\log(\frac{2}{7})=t \times log(0.88)\\\\t=\frac{log(\frac{2}{7})}{log(0.88)}\\\\t=9.799 \approx 9.8$

And so it would take approximately 9.8 years for that (overly expensive) xbox one to be reduced to $200.

~~~Brainliest Appreciated!~~~