W = 2.5 * .2 ^ (0.04 * t) grams as far as i can tell.
if that is correct, then the solution is found as follows:
a)
4 = 2.5 * .2 ^ (.04 * t)
divide both sides of the equation by 2.5 to get:
4/2.5 = .2 ^ (.04 * t)
take the log of both sides of the equation to get:
log(4/2.5) = log(.2 ^ (.04 * t)) is equal to .04 * t * log(.2), the equation becomes:
log(4/2.5) = .04 * t * log(.2)
divide both sides of this equation by .04 * t to get:
log(4/2.5) / log(.2) = .04 * t
divide both sides of this equation by .04 to get:
log(4/2.5) / log(.2) * 1/.04 = t
solve for t to get:
t = -949........
this doesn't make sense, so there is pobably something wrong with the original equation.
under the assumption that .2 really means * 2, i changed the original equation to be:
W = 2.5 * 2 ^ (.04 * t)
when W = 4, the equation becomes:
4 = 2.5 * 2 ^ (.04 * t)
divide both sides of this equation by 2.5 to get:
4/2.5 = 2 ^ (.04 * t)
take the log of both sides of this equation to get:
log(4/2.5) = log(2 ^ (.04 * t))
since log(2 ^ .04 * t)) is equal to .04 * t * log(2), the equation becomes:
log(4/2.5) = .04 * t * log(2)
divide both sides of the equation by log(2) to get:
log(4/2.5) / log(2) = .04 * t
divide both sides of this equation by .04 to get:
log(4/2.5) / log(2) * 1 / .04 = t
solve for t to get:
t = 16.95179763
to solve for 15 grams, just replace W with 15 instead of 4 and do the same procedure.
your answer should be 64.62406252.
the original equation can be graphed and should show the same solutions rounded to at most 3 decimal places.
here's the graph.
