# Exponential Decay Question!?

I don't know how to solve this.

Strontium-90 has a half-life of 25 years. How long would it take 4 mg of it to decay to 0.5 mg?

If someone could show me the steps that would be great!

I have this so far:

0.5=4(1/2)^(t/25)

But I don't know how to solve for t.

Thanks!

Update:

Thank you for those answers, but is it possible to solve without the use of logarithms?

Relevance
• Anonymous

✐Explanation✐

Recall that:

y = abⁿ

This formula is called Exponential Decay formula if 0 < b < 1

You substitute the variables correctly. Divide both sides by 4 first.

1/8 = (1/2)^(t/25)

Rewrite this with logs.

log(1/8) = tlog(1/2)/25

Solve for t.

log(1/8)/[log(1/2)/25] = t

t = 75

first divide both sides by 4 to get rid of that 4 there. So you'll have:

0.125=(1/2)^(t/25)

now, take the log base (1/2) of both sides. from logarithm properties, this will cancel the (1/2) and remove the exponent, leaving the (t/25).

To do this on a calculator for the left side of the equation, divide the log(.125) by log(1/2). The answer for this is 3. Now we have:

3=t/25

t=75