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Logarithms and exponential functions

The mass m grams of a radio active substance is given by the formula m= m0×e^-kt

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Reply 1
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Shas72
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Original post by Shas72
The mass m grams of a radio active substance is given by the formula m= m0×e^-kt

15825520564573153799128628647527.jpg
Reply 2
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Notnek
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What's your question?
Reply 3
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Shas72
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Original post by Shas72
15825520564573153799128628647527.jpg

I got the ans for a and b. The question c iam not understanding. So k=0.02 and m0= 50
Reply 4
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Notnek
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Original post by Shas72
I got the ans for a and b. The question c iam not understanding. So k=0.02 and m0= 50

Do you have any idea for c? Are you able to write down an equation?
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Shas72
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Original post by Sir Cumference
Do you have any idea for c? Are you able to write down an equation?

Its 3.91
Reply 6
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Shas72
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Original post by Sir Cumference
Do you have any idea for c? Are you able to write down an equation?

So I got ln m= -kt+ln m0
Reply 7
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Shas72
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Original post by Sir Cumference
Do you have any idea for c? Are you able to write down an equation?

Iam not able to do question c which is half life of the radioactive substance
Reply 8
Avatar for Notnek
Notnek
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Original post by Shas72
So I got ln m= -kt+ln m0

You don't need k and m0 anymore because you know their values. So first write out the equation with these values substituted in.

You need to find the time taken to get to half its original mass. What's the original mass? So what's half the original mass?
Reply 9
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Shas72
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Original post by Sir Cumference
You don't need k and m0 anymore because you know their values. So first write out the equation with these values substituted in.

You need to find the time taken to get to half its original mass. What's the original mass? So what's half the original mass?

Is the original mass 40.9
Reply 10
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Notnek
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Original post by Shas72
Is the original mass 40.9

How did you get that?
Reply 11
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Shas72
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Original post by Sir Cumference
How did you get that?

From the table of values of t and m
Reply 12
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Notnek
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Original post by Shas72
From the table of values of t and m

No that's the mass at time t = 10. The original mass is the time at t = 0.
Reply 13
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Shas72
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Original post by Sir Cumference
No that's the mass at time t = 10. The original mass is the time at t = 0.

So how will I calculate?
Reply 14
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Shas72
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Original post by Sir Cumference
No that's the mass at time t = 10. The original mass is the time at t = 0.

Do I have to use geometric progression
Reply 15
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Shas72
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Original post by Sir Cumference
No that's the mass at time t = 10. The original mass is the time at t = 0.

So m0 is 50
Reply 16
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Notnek
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Original post by Shas72
So how will I calculate?

You now know (after solving part b) that the estimated equation for mass is this

m=50e−0.02tm=50e^{-0.02t}

So what is m when t = 0? That's the original mass.
Reply 17
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Notnek
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Original post by Shas72
So m0 is 50

Yes. And that's the original mass because it's the value of m when t = 0. So what's half of the original mass? Now make an equation and solve it.
Reply 18
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Shas72
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Original post by Sir Cumference
Yes. And that's the original mass because it's the value of m when t = 0. So what's half of the original mass? Now make an equation and solve it.

Half is 25. How do I make an equation?
Reply 19
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Shas72
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Original post by Sir Cumference
Yes. And that's the original mass because it's the value of m when t = 0. So what's half of the original mass? Now make an equation and solve it.

So I substituted these values in the formula given and it is 25=50× e^-0.02t

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