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Help meeeeeeeeeee pleaseee

Help meeeeeeeeeee pleaseee-example-1
User Toomuchcs
by
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1 Answer

7 votes

Explanation:

your teacher could have explained this better by telling us that A(t) is the remaining amount of the original isotope.

(a)

we start with 200 g and let it do its thing for 25 years.

all we need to do is enter the number of years into the function formula (as this is a college question you are able to work with functions, right ?) and calculate :

A(25) = 200e^(-0.054 × 25) = 200e^-1.35 =

= 51.84805213... g ≈ 51.85 g

after 25 years, about 51.85 g of the sample will be left.

assuming you have a calculator (at least on your computer) that was really "difficult", don't you think ?

(b)

half of the original amount is 200/2 = 100 g.

so, we need to find the value for t so that A(t) = 100.

100 = 200e^(-0.054 × t)

100/200 = 1/2 = 0.5 = e^(-0.054 × t)

ln(0.5) = -0.054 × t

t = ln(0.5) / -0.054 = 12.8360589... years

I assume you need to round to the nearest hundredth here as well :

after about 12.84 years the sample will decay to half of the original amount.

User Andre Carrera
by
8.5k points

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