A motorcycle cost $12,000 when it was purchased. The value of a motorcycle decreases by 6% each year. Find the rate of decay each month and select the correct answer below.

- anonymous

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- anonymous

@Michele_Laino @mathmate @phi

- anonymous

1 year has 12 months so whats 6 divide by 12?

- anonymous

1/2

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## More answers

- anonymous

each month it depreciates by 0.5%

- anonymous

I need one more:)

- anonymous

ok

- anonymous

You decide to put $175 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 3% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

- anonymous

Compound interest formula\[A=P(1+\frac{ r }{ 100 })^n\]\[3000=175(1+0.3)^n\]

- anonymous

300=227.5^n

- anonymous

no it doesnt work like this

- anonymous

\[17.14285714=1.03^n\]

- anonymous

16.64^n

- anonymous

?

- anonymous

log 17.14285714 = 1.23408320596
log 5 = 0.69897000433
1.23408320596/0.069897000433

- anonymous

Thats not an answer choice
8.0111 years
96.1332 years
93.2914 years
94.8377 years

- anonymous

plug in all the in answers to the compound interest formula and try out

- anonymous

? What do you mean?

- anonymous

175(1.03)^n
replace n with all the 4 options, see which one works

- mathmate

or you take log!

- anonymous

i did

- phi

interest rate of 3% per year and is compounded monthly,
that means you work in months (not years) and the interest rate is 0.03/12
the equation you want to solve is
175(1+ 0.03/12)^n = 3000
175(1.0025)^n = 3000
1.0025^n= 17.142857

- anonymous

dayum i forgot something...the interest is compounded monthly!

- mathmate

1.0025^n=3000/175
n log(1.0025)=log(3000/175)
solve for n.

- anonymous

knew something was off

- anonymous

Ok hold on:)

- anonymous

For some reason I got C?? I think I did something wrong

- phi

when you find n, it will be in months
divide by 12 to get years

- anonymous

Was I right?

- phi

what do you get for log(3000/175) ?

- anonymous

1.23408320603

- phi

so you have
n log(1.0025) = 1.23408320603
divide both sides by log(1.0025)
n= 1.23408320603/log(1.0025)
what do you get for n

- anonymous

1.2310056918=n

- anonymous

1138.05283703 i mean

- phi

ok, and that is in months
divide by 12 to get years

- anonymous

94.8377...

- phi

yes

- anonymous

ok so going back to #1 i think sesal gave me the wrong answer??

- anonymous

- anonymous

I got -0.005143% as an swer and she got -0.5% so I dont even know

- phi

if it has a rate of 6% per year, or in this case -6%, as a decimal is -0.06
on a monthly basis, divide by 12: -0.06/12 = -0.005
in percent: -0.5%

- anonymous

Ok! Thanks :) I was just checking!

- anonymous

Solve 3^(2x)=7^(x-1)
I got -7.74293 ??

- phi

if we put your answer into the equation it works

- anonymous

Thanks:)

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