SOLUTION: 6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y? (a) x = 2, y = 4 (b) x=3, y=6 (c) x=4, y=2 (d) x=6, y=3 7)When David was born, his gr

Question 174628This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y?
(a) x = 2, y = 4 (b) x=3, y=6 (c) x=4, y=2 (d) x=6, y=3
7)When David was born, his grandparents deposited $1,000 in a college account that promised 4 percent interest compounded annually for 18 years. Which of the following equations shows the worth of the account when David is 18?
(a) y = 18(4)($1,000)
(b) y = 18(0.04)($1,000)
(c) y = $1,000(0.04)^18
(d) y = $1,000(1.04)^18
Show work thanks so much!This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Answer by ankor@dixie-net.com(12706) (Show Source):
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6) If 4^x = 2^y and 9^x-1 = 3^x+1, which of the following are the values of x and y?
:
In the 1st equation, we can write 4^x as 2^(2x), so we have
2^(2x) = 2^y
Therefore:
2x = y
:
In the 2nd equation, the same:
3^(2(x-1)) = 3^(x+1)
therefore
2(x-1) = x + 1
2x - 2 = x + 1
2x - x = 1 + 2
x = 3
2x = y, therefore
y = 6
:
:
7)When David was born, his grandparents deposited $1,000 in a college account that promised 4 percent interest compounded annually for 18 years. Which of the following equations shows the worth of the account when David is 18?
:
The interest is added to the accumulated amt each year for 18 yrs, therefore:
(d) 1000*(1.04)^18