Iron-59 has a half-life of 45.1 days. How old is an iron nail if the Fe-59 content is 25% that of a new sample of iron? Show all calculations leading to a solution. I am really confused on how to find t here? Can someone help? I can set up the rest of the equation

Didn't I do this a couple days ago for you. Instead of reposting, tell me what you didn't understand about the answer and we can get through it. t is the only unknown in the equation.

http://www.jiskha.com/display.cgi?id=1431110694

I have never had this done for me? I am still confused on how to find t?

To find the age of the iron nail, we need to use the concept of radioactive decay and the half-life of Iron-59 (Fe-59).

The half-life of Iron-59 is given as 45.1 days. This means that after 45.1 days, half of the initial amount of Fe-59 will decay.

To calculate the age of the iron nail, we can set up the equation as follows:

(Fe-59 in iron nail) = (Fe-59 in new sample) * (1/2)^(t/h)

Where:
(Fe-59 in iron nail) is the remaining Fe-59 content in the iron nail
(Fe-59 in new sample) is the initial Fe-59 content in the new sample of iron
t is the time in days (age of the iron nail)
h is the half-life of Fe-59 (45.1 days)

Given that the Fe-59 content in the iron nail is 25% (or 0.25) that of a new sample, we can substitute these values into the equation:

0.25 = 1 * (1/2)^(t/45.1)

Now, let's solve for t. Taking the log of both sides of the equation will help us isolate t:

log(0.25) = log((1/2)^(t/45.1))

Using the logarithmic property, we can bring down the exponent to the front:

log(0.25) = (t/45.1) * log(1/2)

Now, divide both sides of the equation by log(1/2):

t/45.1 = log(0.25) / log(1/2)

Finally, multiply both sides of the equation by 45.1 to solve for t:

t = 45.1 * (log(0.25) / log(1/2))

Using a scientific calculator, evaluate the right side of the equation to find the value of t.