College

An isotope has a half-life of 50 years, and the original amount is 1235 kg.

1. Find a function that models the amount of the isotope after [tex]t[/tex] years.

2. How much will be present after 421 years?

3. After how long will only 215 kg of the sample remain?

Answer :

It will take approximately 350.52 years for only 215 kg of the sample to remain.

The function that models the amount of the isotope after t years is given by:

A(t) = 1235 × [tex]0.5^{(t/50)}[/tex]

where A(t) is the amount of the isotope after t years and 1235 is the original amount.

To find the amount of the isotope after 421 years, we can plug in 421 for t in the function above:

A(421) = 1235 × [tex]0.5^{(421/50)}[/tex] = 12.41

Thus, after 421 years, only 12.41 kg of the isotope will remain.

To find the time at which only 215 kg of the sample will remain, we can solve the equation:

215 = 1235 × [tex]0.5^{(t/50)}[/tex]

for t. This gives us:

t = 50 × log(215/1235) ÷ log(0.5) = 350.52

Learn more about isotopes at

https://brainly.com/question/3014194?referrer=searchResults

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