# Thread: continuous exponential decay

1. ## continuous exponential decay

the main ingredient of napthalene, which is a white hydrocarbon made from coal tar. because of its low boiling point, this chemical evaporates in air readily. the volume, v(t), of a mothball after t weeks is given by v(t)=voe^-0.35t, where vo is the initil volume.
a)if a mothball with a diameter of 2cm is exposed to the air, what volume will reamin after three weeks?
b) graph the function v(t) and use the graph to determine after how many weeks only 10% of the original volume remains.
c) use logarithms to find how long it will take, to the nearest week, for the mothball to reduce to half its original volume.

2. Originally Posted by nithu
the main ingredient of napthalene, which is a white hydrocarbon made from coal tar. because of its low boiling point, this chemical evaporates in air readily. the volume, v(t), of a mothball after t weeks is given by v(t)=voe^-0.35t, where vo is the initil volume.
a)if a mothball with a diameter of 2cm is exposed to the air, what volume will reamin after three weeks?
b) graph the function v(t) and use the graph to determine after how many weeks only 10% of the original volume remains.
c) use logarithms to find how long it will take, to the nearest week, for the mothball to reduce to half its original volume.
a) sub in 2 for vo and 3 for t and calculate.

b) get out your graphing calculator and graph v(t) in Y1 ... don't forget to use x for t and 2 for vo. graph 10% of 2 = .2 in y2 so you can see where the two graphs intersect and solve for t.

c) set the left side equal to 1 (half of 2, right?)
divide both sides by 2
take the natural log (ln) of both sides
solve for t