Math, asked by lhamutenya942, 1 year ago

a sample of 32 grams of an unknown substance has a half -life of 12 years.
1. write an equation to the determine the amount of a substance,s,left after t years.
2. approximately how long will it take for 0.1 grams f the substance to remain (to the nearest year)

Answers

Answered by santy2
0

Step-by-step explanation:

We need to apply the exponential decay function.

The exponential decay function is given as:

The remaining substance A(t) at time t is given by :

A(t) = A(0)e^-kt

The half life t is given by :

-ln 2/k = t

Since we have the half life we can get k.

16 = - ln2 / k

k = - ln 2/ 16

k = - 0.04332

A(0) = the initial amount = 32 grams

1) A(t) = 32e^-0.04332t

2) A(t) = 0.1 gram

0.1 = 32e^-0.04332t

0.1/32 = e^-0.04332t

0.003125 = e^-0.04332t

Taking ln on both sides we have :

ln 0.003125 = - 0.04332t

t = ln 0.003125/-0.04332

= 133.16 years.

To the nearest year is 133 years.

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