$(16$ points$)$ Please use the worksheet named: $$Problem $4\_$butterfly effect$$ for this

problem. Problem statement: The famous butterfly effect states that if a butterfly flaps its

wings in Tahiti, that small event might cause a hurricane to hit Texas. In this problem, we

will illustrate this effect and practice basic operation skills in Excel.

Suppose that weather at time t is always between $0$ and $1$ and is governed by tx $=$A $*$ tx $*$

$(1-$ tx $),$ that is$,$

$1**(1)$t t tx A x x$+=$

Set up a spreadsheet to demonstrate the butterfly effect completing the following $3$ tasks.

$(1)(6$ points$)$ Complete the brown colored cells by calculating tx using the initial value

without deviation, i$.$e$.,$ x$0=0\mathrm{.}9.$

$(2)(6$ points$)$ Complete the blue colored cells by calculating tx using initial value with a very

small deviation value, x$0=0\mathrm{.}900001,$

$(3)(4$ points$)$ Complete the gray colored cells by calculating the percentage difference

between the tx values you calculated above in $(1)$ and $(2).$

$(4)$ Save your Excel file.

After you complete this exercise, please upload both the PDF $($from Problem #$3)$ and your

Excel to Canvas Assignments. $($Please note you need upload two files this week.$)$