Riley is swinging on a swing at the playground. Let t represent time, in seconds, and let represent Riley’s horizontal distance, in inches, from her starting position, as shown in the table. Note: When Riley swings in front of the starting position, is positive, and when Riley swings behind the starting position, is negative. From the table, Riley is moving forward on the interval . It takes Riley seconds to swing forward, back, and then return to her starting position. Riley reaches a maximum distance of inches from her starting position.

n

step-by-step 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)

=====================================

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

=====================================

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).

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.

answer: ay  

fonsi  

dy  

oh

oh no, oh no

oh yeah

diridiri, dirididi daddy  

go

sí, sabes que ya llevo un rato mirándote  

tengo que bailar contigo hoy (dy)  

vi que tu mirada ya estaba llamándome  

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal  

me voy acercando y voy armando el plan  

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal  

todos mis sentidos van pidiendo más  

esto hay que tomarlo sin ningún apuro

despacito  

quiero respirar tu cuello despacito  

deja que te diga cosas al oído  

para que te acuerdes si no estás conmigo

despacito  

quiero desnudarte a besos despacito  

firmo en las paredes de tu laberinto  

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)