Question

What will the area of the wound be on day 8

On what day will the area of the wound be less than one square millimeter

Answer 1

so hmmm if we notice, we have 70, 49, 34.3 and so on

so... from 70 to 49, is 21 less

now, what is 21 of 70? well
`\bf \begin{array}{ccllll} amount&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 70&100\\ 21&x \end{array}\implies \cfrac{70}{21}=\cfrac{100}{x}\implies x=\cfrac{2100}{70}\implies x=30`

so is 30%, that means 49 is the 70%

ok, now, how much is the 70% of 49? well , simply (70/100)*49, which gives us 34.3

how much is the 70% of 34.3, well 0.7*34.3 or 24.01 and so on

so every day, the wound is shrinking by 30%

thus r=30% or 30/100 which is r = 0.30


`\bf A=P(1-r)^d\qquad \begin{cases} d=days\\ A=\textit{current amount}\\ P=\textit{starting value}\\ r=rate\\ ----------\\ P=70\\ r=0.30 \end{cases}\implies A=70(1-0.3)^d \\\\\\ \boxed{A=70(0.7)^d}`