Question

Write a function that models 40mg of a substance that has a half life of 84 days

Answer 1

Answer: The function is M(t) = 40mg*0.992^t

Step-by-step explanation:

Half life refers to the time that a given quantity to reduce to half its initial value.

This is usually a exponential decay, so we want a function of the form:

M(t) = A*r^(*t)

Were t is time, in this case, t is the number of days

A is the initial value

r is the rate of decrease, we will find that for exponential decays r must be a number between 0 and 1. If r is closer to 0, we will have a fast exponential decay, if r is closer to 1 we will have a slower exponential decay.

We have that the initial mass is 40mg, this is at t = 0.

M(0) = A*r^(0) = A = 40mg

So now we have the value of A.

Now, we know that in t = 84, the mass of the substance will be half its initial value, so it will be:

A/2 = 40mg/2 = 20mg

this means that:

M(84) = 40mg*r^(84) = 20mg

r^(84) = 20mg/40mg = 1/2

$r = \sqrt[84]{1/2}$ = 0.992

Then the equation is:

M(t) = 40mg*0.992^t