A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation f (t) = 100 (1/2) ^t/10. After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is 100 (1/2) ^t-3/10. After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

Question

Mathematics

Irene Hayes

10 June, 09:26

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation f (t) = 100 (1/2) ^t/10. After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is 100 (1/2) ^t-3/10. After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

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Answers (1)

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Livia Downs · Answer 1

We are given

m1 = 100 mg

f (t) 1 = 100 (1/2) ^t/10

m2 = 100 mg

f (t) 2 = 100 (1/2) ^t-3/10

The first shipment will have the new equation of

f (t) 1 = 100 (1/2) ^ (t+3) / 10

So,

f (t) 1/f (t) 2

= 100 (1/2) ^ (t+3) / 10 / 100 (1/2) ^ (t-3) / 10

= 100 (1/2) ^[ (t+3) / 10 - (t-3) / 10]

= 100 (1/2) ^ (6/10)

= 65.98%