Question 1143353
if it decays at a constant rate, then you are dealing with an equation of the form f = p * (1 + r) ^ n.


f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.


you start with:
f = 25
p = 100
n = 10


the formula becomes 25 = 100 * (1 + r) ^ 10
divide both sides of this formula by 100 to get:
.25 = (1 + r) ^ 10
take the 10th root of both sides of this equation to get:
.25 ^ (1/10) = 1 + r
subtract 1 from both sides of this equation to get:
.25 ^ (1/10) - 1 = r
solve for r to get:
r = -0.129449437


confirm by replacing r in the original equation with that to get:
25 = 100 * (1 - .129449437) ^ 10
this results in 25 = 25, confirming the solution is correct.


to find the half life, make f = .5 and p = 1 to get:
f = p * (1 + r) ^ n becomes .5 = (1 - .129449437) ^ n
take the log of both sides of the equation to get:
log(.5) = log((1 - .129449437) ^ n)
by the properties of logarithms, this becomes:
log(.5) = n * log(1 - .129449437)
solve for n to get:
n = log(.5) / log(1 - .129449437) = 5


your solution is that the half life of the goo is 5 days.


the goo deteriorates at the constant rate of 12.9449437% per day.
that means it loses 12.9449437% of its mass every day.