Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.

Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.

Now write an equation to find how long it will take for the mass of the radioactive substance to reach 27 grams. Then, solve the equation to find the answer.

Question

Mathematics

Conrad Ramirez

16 July, 05:10

Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.

Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.

Now write an equation to find how long it will take for the mass of the radioactive substance to reach 27 grams. Then, solve the equation to find the answer.

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Answers (1)

Know the Answer?

Julian Donovan · Answer 1

3 hours

Step-by-step explanation:

This situation represents exponential decay which decays 25% every hour.

Rate of decay = r = 0.25

Initial amount = A = 64

Equation

y = a (1 - r) ^ t

where y is final amount = 27g

t is the time = to find

27 = 64 (1 - 0.25) ^t

27/64 = (1 - 0.25) ^t

0.42 = (1 - 0.25) ^t

Take log

ln (0.42) = ln (1 - 0.25) ^t

ln (0.42) = (t) ln (1 - 0.25)

t = ln (0.42) / ln (1 - 0.25)

t = 3.015 hours

t ≈ 3 hours