The average profit in dollars A that your baking business makes when baking n cakes is given by . How many cakes rounded to whole numbers should you bake in order to have a profit of $300?

Question

The average profit in dollars A that your baking business makes when baking n cakes is given by  . How many cakes rounded to whole numbers should you bake in order to have a profit of $300?

Quizplus · Accepted Answer

To find how many cakes should be baked to make a profit of $300, we need to solve the equation 11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11 = 300 for n.

11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11 = 300

Subtracting e^(-0.1n) from both sides:

300 - 11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11 = -11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11 e^(-0.1n)

Dividing both sides by -11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11:

(e^(-0.1n)) / (-0.09076214) - (300 / -11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11) = 1

Using a graphing calculator to find the x-intercepts of the equation y = (e^(-0.1n)) / (-0.09076214) - (300 / -11ec19db_852d_3fa0_9dbe_2fbb66640a6d_TBX8673_11), we get two solutions, n ≈ 16.882 and n ≈ 71.178.

Since we can't bake a fraction of a cake, we need to round these numbers to the nearest whole number.

16 cakes will give us a profit less than $300, while 71 cakes will give us a profit greater than $300. Therefore, we should bake either 17 or 71 cakes to have a profit of $300.

The Average Profit in Dollars a That Your Baking Business