# A chemical substance has a half life of 5 years. A chemist currently has 2000 grams of the substance. If the substance remains untouched, after 25 years, how much of the substance will be left?

Apr 29, 2017

after 25 years there would be $62.5$ grams of the substance

#### Explanation:

Half life refers to the time it takes or half of the substance to decay.

If the half life is 5 years and we begin with 2000 grams, we can create a data list of the decay.

0 years = 2000 grams

5 years = 1000 grams

10 years = 500 grams

15 years = 250 grams

20 years = 125 grams

25 years = 62.5 grams

You can also use the formula

${A}_{f} = {A}_{i} {\left(\frac{1}{2}\right)}^{\frac{t}{h}}$

${A}_{f} =$ Final Amount
${A}_{i} =$ Initial Amount
$t =$ time
$h =$ half-life

${A}_{f} = 2000 {\left(\frac{1}{2}\right)}^{\frac{25}{5}}$

${A}_{f} = 2000 {\left(\frac{1}{2}\right)}^{5}$

${A}_{f} = 2000 \left(\frac{1}{32}\right)$

${A}_{f} = 62.5$