Laura created a website to create T-shirts. In the first month she put up her website she had only a single T-shirt order. Each month she got more orders. Following this function f (n) = 2n-1

How many total orders did she receive over the first year?

Laura received 144 orders over the first year

Solution:

Given function is:

f (n) = 2n - 1

Where, "n" is the month

In the first month she put up her website she had only a single T-shirt order

f (1) = 2 (1) - 1 = 2 - 1

f (1) = 1

There are 12 months in a year

For the second month, and third month and so on, substitute n = 2, 3 and so on

f (2) = 2 (2) - 1 = 4 - 1 = 3

f (3) = 2 (3) - 1 = 6 - 1 = 5

f (4) = 2 (4) - 1 = 8 - 1 = 7

f (5) = 2 (5) - 1 = 10 - 1 = 9

f (6) = 2 (6) - 1 = 12 - 1 = 11

f (7) = 2 (7) - 1 = 14 - 1 = 13

f (8) = 2 (8) - 1 = 16 - 1 = 15

f (9) = 2 (9) - 1 = 18 - 1 = 17

f (10) = 2 (10) - 1 = 20 - 1 = 19

f (11) = 2 (11) - 1 = 22 - 1 = 21

f (12) = 2 (12) - 1 = 24 - 1 = 23

Thus total orders received over first year:

Total orders = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Total orders = 144

Thus she received 144 orders over the first year