4: In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c (z), of mailing a letter weighing z ounces where z is an integer greater than 1

The function that would determine the cost in dollars, c (z), of mailing a letter weighing z ounces is (0.46 + 0.20z)

Explanation:

Weight of the letter = z ounces (z is an integer greater than 1)

cost to mail a letter weighing 1 ounce = $0.46

cost to mail an additional ounce = $0.20

cost to mail z additional ounces = z * $0.20 = $0.20z

Total cost of mailing a letter weighing z ounces = $0.46 + $0.20z

Therefore, cost function, c (z) = 0.46 + 0.2z

c (z) = 0.46 + 0.20 (z - 1)

Explanation:

For letters weighing up to 1 oz $0.46 is charged

For each additional ounce $0.20 is charged

so base cost is $0.46 which should remain constant and should not change.

variable cost is $0.20 which can change according to weight so it should be linked with variable z.

So the required function would be

c (z) = 0.46 + 0.20 (z - 1)

Verification:

Lets verify the above function.

When weight of the letter is 1 oz.

c (1) = 0.46 + 0.20 (1 - 1) = 0.46 + 0.20 (0) = $0.46

When weight of the letter is 2 oz.

c (2) = 0.46 + 0.20 (2 - 1) = 0.46 + 0.20 (1) = $0.66

Hence the function is working correctly.