Question

A sample of a radioactive substance has an initial mass of 58.7 . This substance follows a continuous exponential decay model and has a half-life of 5 hours. (a)Let t be the time (in hours) since the start of the experiment, and let y be the amount of the substance at time t . Write a formula relating y to t. y=__ e^__(t) . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. b)How much will be present in 8 hours? Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

a). Y = y0e^-k(t)

b) Y = 19.4 Unit mass

Explanation:

Y = y0e^-k(t)

Where y is amount present at the time

Y0 is initial amount present at t = 0

Y0 = 58.7

Half life = 5 hours

At half life , y = 58.7/2

At half life , y = 29.35

K = decaying constant.

Let's look fithe value of k

Y = y0e^-k(t)

29.35 = 58.7e^-k(5)

29.35/58.7 = e^-k(5)

0.5 = e^-k(5)

In 0.5 = -k(5)

-0.69314718 = -k(5)

0.138629436 = k

The value present in 8 hours will be

Y = y0e^-k(t)

Y = 58.7e-0.138629436(8)

Y = 58.7e-1.109035488

Y = 58.7(0.329876978)

Y= 19.36377861

To the nearest tenth

Y = 19.4 unit of mass