Question

At Margaret’s bakery the total cost c in dollars of making x loaves of bread is given by the function C(x)=30+1.2x and the function f (x) =

Answer 1

Functions are used to show the relationship between two variables. In this question, the variables are the loaves of bread and the cost. The true statement from the options is:

(c) The cost per loaf of making 50 loaves is less than the cost per loaf of making 40 loaves.

Given that:

$C(x) = 30 + 1.2x$

To determine which of the options is true, we simply test each option.

(a) The cost of 50 loaves is less than the cost of 40 loaves

Calculate C(50) and C(40)

$C(50) = 30 + 1.2 \times 50 =90$

$C(40) = 30 + 1.2 \times 50 =78$

Option (a) is false because $90 > 78$

i.e. It is more expensive to produce 50 loaves than 40 loaves

(b) The cost of 50 loaves is equal to the cost of 40 loaves

In (a), we have that: $90 > 78$

Hence, option (b) is false

i.e. the cost to produce 50 loaves is not equal to the cost of 40 loaves

(c) The cost per loaf of 50 loaves is less than the cost of 40 loaves

Cost per loaf is the total cost divided by the number of loaves i.e.

$Cost = \frac{C(x)}{x}$

For 50 loaves, we have:

$Cost = \frac{C(50)}{50}$

$Cost = \frac{90}{50} = 1.80$

For 40 loaves, we have:

$Cost = \frac{78}{40} = 1.95$

This is true because $1.80 < 1.95$

Hence, the cost per loaf of 50 loaves is less than the cost per loaf of 40 loaves.

Read more about functions at:

brainly.com/question/24314573