/// identify the segment bisector, then find the length of sm, mt, and st.

The segment bisector is RM. The values of SM and MT are both 14 and the value of ST is 28.

To find all of these, you need to find x. You can find x by setting SM and MT equal to each other since they have been bisected.

x + 12 = 8x - 2 > add 2 to both sides

x + 14 = 8x ---> subtract x from both sides

14 = 7x > divide both sides by 7

2 = x

Now that we have x, we can solve all of these.

SM = x + 12

SM = 2 + 12

SM = 14

MT = 8x - 2

MT = 16 - 2

MT = 14

ST = SM + MT

ST = 14 + 14

ST = 28

The Segment bisector is the line with point R on it.

Before you can find the measurements of any of the segments, you must find the value of X. To do this follow these steps:

x+12=8x-2 (they are set equal to each other since they are cut by the bisector)

12=7x-2 (next, subtract X from each side and you get this)

14=7x (Add 2 to each side)

2=x (Divide both sides by 7)

Now that you know x=2, plug in 2 in all the places you see X in the equations.

To find SM:

x+12 (original equation)

2+12 (Plug in 2 for x)

14 (add 12 & 2)

To find MT:

8x-2 (original equation)

8(2)-2 (plug in 2 for X)

16-2 (multiply 8 & 2)

14 (subtract 16 &2)

There are 2 ways to find ST (you'll get the same answer)

1st way to find ST:

x+12+8x-2

2+12+8*2-2 (plug in 2 for X)

14+16-2 (add 12&2, multiply 8&2)

30-2 (Combine 14 &16)

28

2nd way to find ST:

14+14 (this is SM+MT)

28

Your final answers are:

The Segment bisector is the line with point R on it.

SM: 14

MT: 14

ST: 28

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).