Algebra 2 Problems of the Day

Continuing with daily Algebra 2 questions and answers.

More Algebra 2 problems.

January 2018
23. If the function g(x) = ac^x represents exponential growth, which statement about g(x) is false?

(1) a > 0 and b > 1
(2) The y-intercept is (0, a).
(3) The asymptote is y = 0.
(4) The x-intercept is (b, 0).

Answer: (4) The x-intercept is (b, 0).
The function has no x-intercept. And when x = b, then g(x) = ab^b, not 0.
Note that choice (3) and (4) are mutually exclusive, so one of them has to be false.
Since it is exponential growth, a > 0 and b > 1. And when x = 0, g(x) = ab⁰ = a.



24.At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is a_n = 25,000 + (n - 1)1000. Which rule best represents the equivalent recursive formula?
(1) a_n = 24,000 + 1000n
(2) a_n = 25,000 + 1000n
(3) a₁ = 25,000, a_{n - 1} + 1000
(4) a₁ = 25,000, a_{n + 1} + 1000

Answer: (3) a₁ = 25,000, a_{n - 1} + 1000
In the recursive formula, each term is the sum of the term before it (a_n-1) plus 1000, which is choice (3).
Note that choices (1) and (2) are not recursive formulas.



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More Algebra 2 problems.