1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
1+4=5
2+5=7
5+7=12
3+6=9
12+9=21
I do not see21 up here so please cheek your question again or please change the 19 to a 21
Yes for the first one and I think yes for 2nd
Answer:
Blues Paints = 2.45 pints
Step-by-step explanation:
Let's generate an expression that would relate all the variables given:
Total pints of paints used:
9.8 = white + blue
Pints of white paint used:
= 3/4 of 9.8
=0.75 * 9.8
=7.35
Number of pint of BLUE PAINTS used:
9.8 = White Paints + Blue Paints
9.8 = 7.35 + Blue Paints
Blue Paints = 9.8 - 7.35
Blues Paints = 2.45
Kate used 2.45 pints Blues Paints for her bedroom
