Tavon has a gift card for $ 50 that loses $ 2 for each 30-day period it is not used. he has another gift card for $ 40 that loses $ 1.50 for each 30-day period it is not used. a. write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. what will the value of each card be when they have equal value?

So we know that month 1: gift card 1: 50$ gift card 2: 40$

month 2: gift card 1: 48 gift card 2: 38.50

month 3: gift card 1: 46 gift card 2: 37

month 4: gift card 1: 44 gift card 2: 35.5

month 5: gift card 1: 42 gift card 2: 34

month 6: gift card 1: 40 gift card 2: 32.5

month 7: gift card 1: 38 gift card 2: 31

month 8: gift card 1: 36 gift card 2: 29.5

month 9: gift card 1: 34 gift card 2: 28

month 10: gift card 1: 32 gift card 2: 26.5

month 11: gift card 1: 30 gift card 2: 25

month 12: gift card 1: 28 gift card 2: 23.5

month 14: gift card 1: 26 gift card 2: 22

month 15: gift card 1: 24 gift card 2: 20.5

month 16: gift card 1: 22 gift card 2: 19

month 17: gift card 1: 20 gift card 2: 17.5

month 18: gift card 1: 18 gift card 2: 16

month 19: gift card 1: 16 gift card 2: 14.5

month 13: gift card 1: 14 gift card 2: 13

month 13: gift card 1: 12 gift card 2: 11.5

month 14 gift card 1: 10 gift card 2: 10

MONTH 14 THEY ARE EQUAL

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752