1. consider the following game, called matching pennies, which you are playing with a friend. each of you has a penny hidden in your hand, facing either heads up or tails up (you know which way the one in your hand is facing). on the count of "three," you simultaneously show your pennies to each other. if the face-up side of your coin matches the face-up side of your friend’s coin, you get to keep the two pennies. if the faces do not match, your friend gets to keep the pennies. (lo1) a. who are the players in this game? what are each player’s strategies? construct a payoff matrix for the game. b. does either player have a dominant strategy? if so, what? c. is there an equilibrium? if so, what? frank, robert. principles of microeconomics (p. 259). mcgraw-hill higher education. kindle edition.

a: the players are you and your friend. No, there are no dominant strategies. Recall that a dominant strategy is one that yields a higher payoff regardless of the strategy chosen by the other player. In this game, if your friend plays one side, you will match that side; however, if you match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff. No, there is no equilibrium. As discussed in part b, if your friend plays one side, you will match that side; however, ifyou match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff

Step-by-step explanation:

tube or goog would be a great resource to with that question

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).