Davis notices that his hair is decreasing exponentially at a rate of 10% per year. If he starts with 100,000 hairs on his head, how many hairs will he have after 3 years ?

Answer 1

100000 * 0.9^3 = 72900

Answer 2

Use h=h₀e^-kt as the law to use where h=amt of hair, h₀ = 100000. First need to solve for k so for a 10% reduction after 1 year 90000 = 100000 e^-k since t=1 yr solving for k gives -k= ln.9 = -.1053 or k = .1053. Now to find how much hair there is after 3 years h= 100000 e^{- 3(.1053)} or h= 100000 e^{- .3159} and h= 72913 hairs after 3 years.