How long will it take for polonium-218 to decay to 30%?

[Edgar92]

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

 

[Edgar92]

I realize this is simple but I am forgetting and don't have my textbook

 

[Mentallic]

You've already done this:

$$0.3=\frac{100(0.5)^t}{3.1}$$

$$\frac{0.3}{100}=\frac{(0.5)^t}{3.1}$$

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

and remember the log laws that if $$a^x=b$$ then $$log_ab=x$$

and finally... (which you tried to show in the relevant equations but the equation was surprisingly cut short) ... $$log_cb=\frac{log_ab}{log_ac}$$

 

[Edgar92]

The exponent is divided by 3.1, not the equation

 

[Char. Limit]

In that case, just use the log-exp switchy thingy immediately.

 

[Dick]

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?

 

[Mentallic]

The exponent is divided by 3.1, not the equation

The log laws still apply.