Question

A radioactive substance is decaying at a rate of 6% every hour. The scientist's original sample was 200 grams. Write an equation to model the amount of the substance after any number of hours, ( t ).

f(t) = 200 × (1 - 0.06)^t
How much substance remains after one full day (24 hours)? Round your answer to the nearest tenth.

a) 5.3 grams
b) 11.2 grams
c) 1.6 grams
d) 42.4 grams

Answer 1

Using the exponential decay equation, the amount of a radioactive substance remaining after 24 hours was calculated to be approximately 11.2 grams, with option (b) being the correct answer.

Step-by-step explanation:

The question involves the exponential decay of a radioactive substance. Given a decay rate of 6% per hour and an initial sample size of 200 grams, we use the equation f(t) = 200 × (1 - 0.06)^t to model the amount of substance remaining after any number of hours, t. To find out how much substance remains after a full day (24 hours), we substitute t with 24:

f(24) = 200 × (1 - 0.06)^{24}

Calculating this, we get approximately 11.2 grams, so the correct answer is (b) 11.2 grams.