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) = ab^{0} = 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) a_{1} = 25,000, a_{n - 1} + 1000
(4) a_{1} = 25,000, a_{n + 1} + 1000
*

**Answer: (3) a _{1} = 25,000, a_{n - 1} + 1000**

In the recursive formula, each term is the sum of the term before it (

*a*) plus 1000, which is choice (3).

_{n-1}Note that choices (1) and (2) are not recursive formulas.

Comments and questions welcome.

More Algebra 2 problems.

## 2 comments:

Thanks for helping me prep

You're welcome.

I glad this is useful for someone.

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