Question

The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 95 grams of this substance. Construct an exponential model for the amount of the substance remaining on a given day. Use your model to determine how much of the substance will be left after 4 days

Answer 1

Answer:

Exponential model

Y = y0e-0.693(t½)

Amount remaining after 4 days

5.9413 grams

Step-by-step explanation:

The formula will he given by

Y = y0e-k(t½)

The half life t½ for this radioactive substance is a day.

Initial mass y0 = 95 grams

Mass after one day = 95/2

Mass after one day = 47.5

.

Value of the decay constant k is not given, let's look for k.

Y = y0e-k(t½)

47.5= 95e-k(1)

47.5/95= e-k(1)

0.5= e-k(1)

In 0.5 = -k

-0.693= -k

0.693 = k

Y = y0e-0.693(t½)

Amount remaining after 4 days

Y = y0e-0.693(t½)

Y = 95e-0.693(4)

Y= 95e-2.772

Y= 95(0.06254)

Y= 5.9413 grams