Going round-trip with the world’s fastest land animal according to the travel almanac, the world’s fastest land animal is the cheetah. it can travel at up to 70 mph. think of this scenario: a cheetah sitting under a tree sprints toward its prey at 70 mph. it runs back to its initial spot by the tree at a modest 40 mph. the cheetah has embarked on a round-trip. going from point a to point b, the cheetah traveled at an average rate of 70 mph. returning to point a, the cheetah traveled at an average rate of 40 mph. can we say that this cheetah’s average rate was 55 mph? that’s one of the things you’ll determine as you work to complete this task. make a conjecture. what do you think the answer will be? directions: complete each of the following tasks, reading the directions carefully as you go. be sure to show all work where indicated and to insert images of graphs when needed. make sure that all graphs or screenshots include appropriate information, such as titles and labeled axes. if your word processing program has an equation editor, you can insert your equations here. otherwise, print this activity sheet and write your answers by hand. you will be graded on the work you show, or your solution process, in addition to your answers. make sure to show all of your work and to answer each question as you complete the task. type all of your work into this document so you can submit it to your teacher for a grade. you will be given partial credit based on the work you show and the completeness and accuracy of your explanations. your teacher will give you further directions as to how to submit your work. you may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. before you begin, recall the formula that relates distance, rate, and time. the distance formula is given by d = rt, where: d represents distance. common units are miles or feet. t represents time. common units are hours

step-by-step explanation:

the answer is c hope it

step-by-step explanation:

found it xd it ok yt

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).