Simple exponent variable

  • Thread starter Edgar92
  • Start date
  • #1
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1. The problem statement, all variables
a sample polonium-218 decays at A(t)=100(.5)^t/3.1
determine how many minutes it will take to decay to 30%

2. Homework Equations
log(a)/log(b)


3. The Attempt at a Solution

.3=100(.5)^t/3.1
.3/100=.5^t/3.1
 

Answers and Replies

  • #2
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I realize this is simple but I am forgetting and don't have my textbook
 
  • #3
Mentallic
Homework Helper
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You've already done this:

[tex]0.3=\frac{100(0.5)^t}{3.1}[/tex]

[tex]\frac{0.3}{100}=\frac{(0.5)^t}{3.1}[/tex]

So why don't you follow the same kind of procedure and multiply by 3.1 :smile:

and remember the log laws that if [tex]a^x=b[/tex] then [tex]log_ab=x[/tex]

and finally... (which you tried to show in the relevant equations but the equation was surprisingly cut short) ... [tex]log_cb=\frac{log_ab}{log_ac}[/tex]
 
  • #4
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The exponent is divided by 3.1, not the equation
 
  • #5
Char. Limit
Gold Member
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In that case, just use the log-exp switchy thingy immediately.
 
  • #6
Dick
Science Advisor
Homework Helper
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The exponent is divided by 3.1, not the equation
Fine. But you can still take the log of both sides and get a linear equation in t, can't you?
 
  • #7
Mentallic
Homework Helper
3,798
94
The exponent is divided by 3.1, not the equation
The log laws still apply.
 

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