Create a Graph Now that you are familiar with the way a demand curve is graphed, you will create your own graph to submit to your instructor.

Step 1: Launch the data generator to get started. Print or copy the data table to use in the next step.

Step 2: Create a demand graph:

Correctly label the x axis and y axis with the terms price and quantity.
Assign values for price and quantity along each axis. Consider the numbers in your data table and the size of your graph. For example, you may want to label price in increments of 25.
Create a title for your graph by choosing a good or service for the data to represent.
Using the data table from Step 1, plot a demand curve and label the curve “D”.
Step 3: Add a curve to your graph that represents an increase in demand. Label the new curve “D1.”

Step 4: In a few sentences, explain a situation that could have resulted in the demand increase. Be sure to:

Make your situation specific to the product or service you chose in Step 2.
Use at least one factor from the acronym TRIBE in your explanation.
Step 5: Add another curve to your graph that represents a decrease in demand. Label the new curve “D2.”

Step 6: In a few sentences, explain a situation that could have resulted in the demand decrease. Be sure to:

Make your situation specific to the product or service you chose in Step 2.
Use at least one factor from the acronym TRIBE in your explanation.

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).

yes

step-by-step explanation:

they have to be opposite and reciprocal of eachother.

noncoplanar points are points that do not lie on the same line.