100 kg decays to 59 kg in 90 yrs; find amt after 180 yrs

[kalpana]

Solve for t. Assume k is a nonzero constant. (Note: To enter P0, type P_0.)
P = P0 e^kt
what i did is
p/p_0=e^kt
taking log on both sides
ln(p/p_0)=kt
t=(ln(p/p_0))/k
is this the correct answer?

One hundred kilograms of a radioactive substance decays to 59 kg in 90 years. How much remains after 180 years?
what i did is
59=100e^-kt
59=100e^-k90
59/100=e^-90k
logging both sides
ln(59/100)=-90k
k=-.005862586
suppose after 180yr
p=100e^-.005862586*180
lnp/100=-1.055265484
now i didn't know what to do?
plz help me through these problems

 

[mmm4444bot]

Re: pre calculus

Solve for t.
P = P0 e^kt
t=(ln(p/p_0))/k
is this the correct answer?

YES!

The following is another form of the same thing.

t = (1/k) * ln(P/Po)

59=100e^-kt

Some textbooks/teachers use two different formulas and they say that the symbol k is ALWAYS a positive number; they use one formula for exponential growth (with no negative sign in front of k), and another formula for exponential decay (with a negative sign in front of k).

Maybe this is why you typed a negative sign in front of k.

I don't do it that way. I use the SAME formula for both exponential growth problems and exponential decay problems.

P = Po e^(kt)

The symbol k stands for a POSITIVE number when working with exponential GROWTH problems.

The symbol k stands for a NEGATIVE number when working with exponential DECAY problems.

In other words, the sign of this number is what determines whether this formula models growth or decay.

k=-.005862586

This negative value is CORRECT!

However, it is ONLY correct when using the formula without the negative sign in front of k.

p=100e^-.005862586*180
lnp/100=-1.055265484 ? THIS LINE IS GARBAGE
now i didn't know what to do?

You correctly got this far:

p = 100 e^(-0.00586 * 180)

Have you forgotten what you are looking for?

The symbol p stands for the amount in kilograms of the radioactive stuff after 180 years.

You already found an expression for it: 100 e^(-0.00586 * 180)

You should realize that the next step is to simply plug this information into a calculator to obtain the value of p.

Please let us know if you need more guidance.

Cheers,

~ Mark

 

[kalpana]

Re: pre calculus

i tried answer for both of the question but it says that it's not correct

 

[mmm4444bot]

Re: pre calculus

... it says that it's not ...

Huh?

The book says that the calculator is not correct?

I don't understand what you're trying to say here.

Please tell me your answer for the second problem.

Also, please tell me what your source says for both answers.

~ Mark