The forward differences for this data is 1, 1, 1, 1, 1, 1 (since 10 - 9 = 1, 11 - 10 = 1, etc). Since we only need one iteration of differences, a linear polynomial will fit the data exactly.
Answer:
Step-by-step explanation:
Method 1:
First do the operation inside parenthesis
2*(4-3) = 2*1 = 2
Method 2:
Use distributive property: a*(b +c) = a*b + a*c
2*(4-3) = 2*4 - 2*3
= 8 - 6
= 2
a = amount invested at 5%
b = amount invested at 2%
now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.
![a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}](https://tex.z-dn.net/?f=a%20%2B%20b%20%3D%2020000%5Cimplies%20b%20%3D%2020000-a%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7B5%5C%25%20of%20a%7D%7D%7B%5Cleft%28%20%5Ccfrac%7B5%7D%7B100%7D%20%5Cright%29a%7D%5Cimplies%200.05a~%5Chfill%20%5Cstackrel%7B%5Ctextit%7B2%5C%25%20of%20b%7D%7D%7B%5Cleft%28%20%5Ccfrac%7B2%7D%7B100%7D%20%5Cright%29a%7D%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%200.02b%5C%5C%5C%5C%20%5Cstackrel%7Bsubstituting%7D%7B0.02%2820000-a%29%7D%20%5Cend%7Barray%7D)
now, we know the total of earned interest is 550 bucks, so then
1.5 liters all together!
Hope that helps!
-procklownyt
