## Friday, April 20, 2018

### Algebra 2 Problems of the Day

Continuing with daily Algebra 2 questions and answers.

More Algebra 2 problems.

January 2018
21. What is the inverse of f(x) = -6(x - 2)?

(1) f-1(x) = -2 - x/6
(2) f-1(x) = 2 - x/6
(3) f-1(x) = 1 / (-6(x - 2))
(4) f-1(x) = 6(x - 2)

Answer: (2) f-1(x) = 2 - x/6
Inverse operations. Divide by negative six, then add two.
x = -6(f-1(x) - 2)
x / (-6) = f-1(x) - 2
2 - x/6 = f-1(x).

22. Brian deposited 1 cent into an empty non-interest bearing bank account on the first day of the month. He then additionally deposited 3 cents on the second day, 9 cents on the third day, and 27 cents on the fourth day. What would be the total amount of money in the account at the end of the 20th day if the pattern continued?
(1) \$11,622,614.67
(2) \$17,433,922.00
(3) \$116,226,146.80
(4) \$1,743,392,200.00

Do not answer the 20th term in the geometric sequence. They are looking for the sum of the first 20 terms.
The formula for finding the sum of the first n terms in a geometric sequence is

Sn = (a1(1 - rn)) / (1 - r),

where n is the number of terms, r is the common ratio, and a1 is the initial term.
In this question, the common ratio is 3, because the sequence goes 1, 3, 9, 27 ...
So the sum is (1 * (1 - 320)/(1 - 3) = 1743392200, which is the number of cents. Divide this by 100 to convert it to dollars, or \$17,433,922.00.
Alternatively, you could have used .01 for the initial term in the formula, which would have given you the answer immediately.

Comments and questions welcome.

More Algebra 2 problems.