$$ 3,9,27,81 \ldots $$ Which exponential function describes the given sequence? $$ y=(-3)^{x} $$ $$ y=\left(-\frac{1}{3}\right)^{x} $$ $$ y=3^{x} $$ $$ y=\left(\frac{1}{3}\right)^{x} $$

Question

UpStudy AI · Accepted Answer

To determine which exponential function describes the given sequence $$ 3, 9, 27, 81, \ldots $$, we first need to analyze the pattern in the sequence.

1. **Identify the pattern:**
   - The first term is $$ 3 $$.
   - The second term is $$ 9 $$, which is $$ 3^2 $$.
   - The third term is $$ 27 $$, which is $$ 3^3 $$.
   - The fourth term is $$ 81 $$, which is $$ 3^4 $$.

From this, we can see that each term can be expressed as a power of $$ 3 $$:
- $$ 3 = 3^1 $$
- $$ 9 = 3^2 $$
- $$ 27 = 3^3 $$
- $$ 81 = 3^4 $$

2. **Generalizing the pattern:**
   The $$ n $$-th term of the sequence can be expressed as:
$$
a_n = 3^n
$$
where $$ n $$ starts from $$ 1 $$.

3. **Identifying the correct function:**
   The exponential function that describes this sequence is:
$$
y = 3^x
$$

Now, let's check the other options to confirm that they do not fit the sequence:
- $$ y = (-3)^x $$: This would yield alternating signs and is not consistent with the sequence.
- $$ y = \left(-\frac{1}{3}\right)^x $$: This would also yield alternating signs and fractions, which does not match the sequence.
- $$ y = \left(\frac{1}{3}\right)^x $$: This would produce decreasing values approaching zero, which does not match the increasing sequence.

Thus, the correct exponential function that describes the given sequence is:
$$
\boxed{y = 3^x}
$$
The correct exponential function is $$ y = 3^x $$.

Which exponential function describes the given sequence?

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions