gary and devonte are doing an experiment with an electroscope. they bring a negatively charged rod close to the top of a charged electroscope. the two metal pieces of the electroscope were spread apart already, but now they move farther away from each other. gary says that the experiment proves that the electroscope had a negative charge before they started experiment, but devonte disagrees and said it must have had a positive charge since the metal pieces moved farther away. who is right and why?

the electroscope had a positive charge before the experiment started. the negatively charged rod attracts the electrons in the electroscope and makes the metal pieces spread further apart.

the electroscope had a positive charge before the experiment started. the negatively charged rod repels protons and makes the metal pieces spread further apart.

the electroscope had a negative charge before the experiment started. when the negatively charged rod comes near the electroscope more electrons are repelled down to the metal pieces and the metal pieces move farther away from each other.

the electroscope had a negative charge before the experiment started. the negatively charged rod attracts electrons and causes the metal pieces to move further apart.

The electroscope had a negative charge before the experiment started.  When the negatively charged rod comes near the electroscope more electrons are repelled down to the metal pieces and the metal pieces move farther away from each other.

 Step-by-step explanation: First of all, how we know the answer is not A or B is because unlike charges attract each other which means the metal pieces would not spread out. Now that we narrowed it down to C and D we can find the answer, In answer choice D it states that the negatively charged rod attracted the electrons from the electroscope, if that happened then something would happen to the rod, not the electroscope. In answer choice C it says that the rod repels the electrons downward on to the metal pieces, which would cause the metal pieces to spread out since they are both negative. Sorry, I'm not the best with explaining, I hope you understand.

mx+89b(-98)nb

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).