Question

Kate is knitting a 90-inch scarf at the rate of 8 inches per day. Write a rule in function notation to find the number of inches she has left to knit at the end of any given day. Let d represent the number of days spent knitting.

Answer 1

lets let Sl mean scarf left to knit, r rate and d day. At the start she has:

Sl = 90

90 inches left. At the end of the first day, she has knitted 8 inches so she has:

Sl = 90 - 8

90 total inches, minus 8 inches she knitted. At the end of another days knitting she has

Sl = 90 - 8(from the first day) - 8(from the second day)

so she has

Sl = 90 - 2(8)

and on the third day she knits another 8, so she has knitted a total of 3 lots of 8, 3 x 8

Sl = 90 - 3(8)

so as each day goes by, she knits another lot of 8, so we can write the equation as

Sl = 90 - d(8)

where d is the amount of days. d = 1 for day 1, d = 2 for day 2, d = 3 for day 3 and so on.

to put this in function notation is to notice that the variable Sl depends on d. so we write

Sl(d) = 90 - 8d

so how many inches does she have left after 5 days?

well:-

Sl(5) = 90 - 8 x 5 = 50 inches left

Whats really cool about this is that we can solve the equation to find out how long it takes to knit the entire scarf! so when the scarf is knitted, the "scarf left" "Sl(d)" is 0 so:

0 = 90 - 8d
8d = 90

d = 90/8 = 11.25 days :)