At the beginning of an experiment, a scientist has 340 grams of radioactive goo. After 150 minutes, her sample has decayed to 5.3125 grams.

Question

I have to find the exponential formula for (G(t), the amount of goo remaining at the time t.

then I have to find how much goo will remain after 68 minutes?

and how many minutes will it take until there are 170 grams of goo remaining?

Answer 1

t=0, g=340

t=150, g=3.125

g=ab^t

=340b^t

3.125=340b^150

b^150= 3.125/340

b = the 150th root of 3.125/340= (.6625/68)^1/150

g(t)= 340(.6625/68)^t/150

g(68)= 340(.6625/68)^68/150

= 340(.6625/68)^34/75

g(t)=170=340(.6625/68)^t/150

(.6625/68)^t/150 = 1/2

t/150 = log_.6625/68.5

t= 150log_.6625/68.5 minutes to reach 170 grams

= 150ln.5/ln(.6625/68)

use a calculator wth natural log function