Jake bought another computer for $3250. This computer depreciates at a rate of 11% every year. Write a model and predict when the computer will be worth $200.

My model: 200 = 3250(.89)^x
Is this correct? And how do I solve for x (time)?

Question

Jake bought another computer for $3250. This computer depreciates at a rate of 11% every year. Write a model and predict when the computer will be worth $200.

My model: 200 = 3250(.89)^x 
Is this correct? And how do I solve for x (time)?

nnesha · Answer

yep lO_Oks right :-)
 in order to solve for x first u should divide by 3250 both sides

anonymous · Answer

@Nnesha I got a really long decimal, so from there I set the decimal equal to (.89)^x, but how do I solve for the exponent? I can't divide by (.89) right?

nnesha · Answer

yep you can't divide by .89 bec of exponent 
200/3250 =  .0615  $$\huge\rm .0615 = (.89)^x$$
now take "ln" both side then you can use  power rule 
 
power rule $$\large\rm ln x^y = y \ln x$$

rational · Answer

good question!

anonymous · Answer

@Nnesha So divide by ln on both sides?

anonymous · Answer

@Nnesha Oh! I understand now! Thank you very much! And thank you @rational

rational · Answer

hey sure ?

rational · Answer

you need to use calculator

anonymous · Answer

@rational Yes I understand that and I got the correct answer

rational · Answer

sounds great! whats your final answer ?

anonymous · Answer

@rational 23.9 years

rational · Answer

looks perfect!