What is 1 = 128 times 1/2 to the power of x and how do i solve it? kid friendly explanation : )

Q1) jin loves carrot yesterday she ate ½ of here carrots and today she ate 2/3 of the remaining carrots. she then discover that she has 12 carrots left. yesterday she must has started with carrots? a)36 b)48 c)60 d)72

A) if $50000 is invested in a bank account that pays 9.3% of interest compounded on a six-monthly basis, how much money will be in the account after 3 and 12 years? b) if matusalen's father had put $2.0 in the bank when he was born and there, how long would matusalen have had to his death (969 years later) if the interest was 7% per year composed each month and weekly?

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota