Ahalf-life is the amount of time it takes for a radioactive substance to decay by half. in general, we can use the
equation a = p (1 / 2) ^t
for the amount of the substance remaining after tt half-lives.
a. what does p represent in this context?
b. if a half-life is 20 hours, rewrite the equation to give the amount after h hours.
c. use the natural logarithm to express the original equation as having base e.
d. the formula you wrote in part (c) is frequently referred to as the "pert" formula, that is, pe^rt
. analyze the
value you have in place for r in part (c). what do you notice? in general, what do you think r represents?
e. jess claims that any exponential function can be written with base e; is she correct? explain why.