there are 2 questions
1. Three of the potions the Plaid Wizard often works with are Star Sand, Diamond Dirt, and Liquid Light. If the formula that represents the amount of Star Sand in a creature's body is given by S(t)=16⋅(1/7)^t, what is the half-life of Star Sand? Enter your answer as a number rounded to two decimal places, like this: 4.25
2. When the Plaid Wizard uses a potion on a creature, he needs to know how long it takes for the potion to wear off. He uses the general formula for the half-life of a substance to analyze these types of situations. Explain, in a few sentences, how the Wizard can rearrange a formula like Q(t)=a⋅b^t in order to calculate the half-life of a substance.
the half-life is x, such that (1/7)^x = 1/2
x log 1/7 = log 1/2
x = log2/log7 = 0.356
That is, (1/7)^(0.356t) = (1/2)^t
as with the first problem, you want a*b^t = a*(1/2)^(kt)
so k = logb/log(1/2) = -logb/log2 = -log2b
Then the half-life is 1/k