Question

he​ half-life for a link on a social network website is 2.6 hours. Write an exponential function T that gives the percentage of engagements remaining on a typical link on the social network website after t hours. Estimate this percentage after 5.5 hours.

Answer 1

Answer:

% Remaining$= [1-(1/2)^{\frac{t}{2.6}}]x100$

And replacing the value t =5.5 hours we got:

% Remaining$= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%$

Step-by-step explanation:

Previous concepts

The half-life is defined "as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not".

Solution to the problem

The half life model is given by the following expression:

$A(t) = A_o (1/2)^{\frac{t}{h}}$

Where A(t) represent the amount after t hours.

$A_o$ represent the initial amount

t the number of hours

h=2.6 hours the half life

And we want to estimate the % after 5.5 hours. On this case we can begin finding the amount after 5.5 hours like this:

$A(5.5) = A_o (1/2)^{\frac{5.5}{2.6}}$

Now in order to find the percentage relative to the initial amount w can use the definition of relative change like this:

% Remaining = $\frac{|A_o - A_o(1/2)^{\frac{5.5}{2.6}}|}{A_o} x100$

We can take common factor $A_o$ and we got:

% Remaining$= [1-(1/2)^{\frac{t}{2.6}}]x100$

And replacing the value t =5.5 hours we got:

% Remaining $= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%$