Question 233600
{{{N[t]= N[0]*e^(-0.125*t)}}} is what I believe your formula looks like after putting it through algebra.com formula generator.


Just put three { in front and three } in back of the formula to see what algebra.com formula generator will make your formula look like.


Example:


formula is: N[t]= N[0]*e^(-0.125*t)


Algebra.com formula generator makes it look like {{{N[t]= N[0]*e^(-0.125*t)}}}


Anyway, your answer looks like it is 11 days to the nearest integer.


The full answer shows up as 11.09035489


Here's how it works:


N[t] is what you are looking for.


If you want to know how long it will take for 75% of the wound to heal, then you need to translate that into the percent of the wound that didn't heal which would make that 25%, because the formula is set up to show you the amount of skin remaining to be healed.


If you allow the original wound to be 1 square cm, then 25% of that would be .25 square cm. 


N[0] would be 1
N[t] would be .25 


Your formula of:


N[t]= N[0]*e^(-0.125*t) would become:


.25 = 1*e^(-0.125*t)


This becomes:


.25 = e^(-0.125*t)


Take the natural log of both sides to get:


ln(.25) = ln(e^(-0.125*t))


This becomes:


ln(.25) = -.125*t*ln(e)


since ln(e) = 1, this becomes:


ln(.25) = -.125*t


divide both sides by -.125 to get:


t = ln(.25)/(-.125)


solve for t to get:


t = 11.09035489


I confirmed the answer is good by plugging into the original equation and solving.