I need help with the following question below, thank you!

Question

Assume that whenever you wash a pair of blue jeans they lose 4% of the color they had before they were washed. How much of the original color would be left after 10 washings? Suppose that you buy a new pair of jeans and decide to wash them enough times so that only 25% of the original color remains. How many times must you wash them?

Answer 1

N(t) = N₀·0.96^t, where t is number of wash.

N(10) = N₀·0.96¹⁰ = 0.6648N₀

Now if N(t) = 0.25N₀ = N₀·0.96^t; 0.96^t = 0.25; t = ln(0.25)/ln(0.96) ≈ 34

Answer 2

Use the equation A = 100(1-.04)ⁿ to get the percent of color left after n washes.

1) A = 100(0.96)¹⁰ = 66.48% of color left

2) 25 = 100(0.96)ⁿ

0.25 = (0.96)ⁿ

log(0.25) = nlog(0.96)

n = log(0.25)/log(0.96) = 33.959 ≈ 34 times