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prohojiy [21]
3 years ago
6

Given the function f(x) = 2(3)^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Mathematics
1 answer:
sleet_krkn [62]3 years ago
8 0

Average rate of change can be calculated by determining the rate of change at x = a, and at x = b

f’(x) =2 (3^x) ln(3)

f’(0) = 2 ln(3)

f’(1) = 6 ln(3)

f’(2) = 18 ln(3)

f’(3) = 54 ln(3)

Average:

at section A = [6 ln(3) – 2 ln(3)]/1 = 4 ln(3)

at section B = [54 ln(3) – 18 ln(3)]/1 = 36 ln(3)

section B is 9 times larger.

Based from the f’(x), f’(x) varies as the power of x. so the greater of value of x, the greater the rate of change.

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A small business makes cookies and sells them at the farmer's market. The fixed monthly cost for use of a Health Department–appr
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Answer:

Cost function:

C(x)=790+2.88x

Revenue function

R(x)=6x

Profit function

P(x)=3.12x-790

Dozens needed for a specific profit P

x=\dfrac{P-790}{3.12}

If 150 dozen cookies are sold the profit is negative, so the business is loosing $322.

Step-by-step explanation:

We can list the costs as:

- Fixed monthly cost, $790/month.

- Variable costs, $0.24/cookie, which are (12*0.24) = $2.88 a dozen.

Then, we can write the cost function C(x) as:

C(x)=790+2.88x

being C(x): the monthly cost and x: the number of dozens produced per month.

The revenue can be calculated as the price ($6 a dozen) multiplied by the number of dozens x:

R(x)=6x

The profit can be calculated substracting the total cost C(x) from the revenue R(x).

P(x)=R(x)-C(x)\\\\P(x)=(6x)-(790+2.88x)=(6-2.88)x-790\\\\P(x)=3.12x-790

The number of cookies (in dozens) that must be produced and sold for a monthly profit can be calculated from the previous equation for P(x).

For a monthly profit P, the number of dozens that need to be sold are:

P=3.12x-790\\\\P+790=3.12x\\\\\\x=\dfrac{P-790}{3.12}

If 150 dozen cookies are sold, the profit made is:

P(150)=3.12(150)-790=468-790=-322

The profit is negative, so the business is loosing $322.

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