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Choice C

Step-by-step explanation:

$80 to 5 hours

Divide both numbers by 5 to find the unit rate:

$16 to 1 hour, or 16 to 1

For x hours, the pay, y, is y = 16x.

Choice A is true.

Look at choice B.

When x = 5, y = 80.

This is correct because we are given that information.

The process is to multiply the hours by 16.

For x hours, y = 16x (from choice A)

For x = 7, y = 7 * 16

Choice B works.

Look at choice C.

We need a proportion. The left side is the ratio 80/5, meaning $80 for 5 hours of work. Notice that the first number in the ratio is dollars, and the second number is hours. Now we need another ratio written in the same order to set up a proportion. x dollars is to 7 hours. This is the ratio x/7. The correct proportion is

80/5 = x/7

Choice C is 80/5 = 7/x

Choice C is incorrect.

Look at choice D.

The graph shows that for 5 hours, the pay is $80, so by looking up x = 7, you can find the correct amount of pay.

Choice D works.

Choice C

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.