Question

Consider the function g(x)=15x
.

Starting with 3, provide the next five x-values that can be used to approximate 1511√
.

(2 points)
3,
,
,
,
,

Answer 1

To approximate \(\sqrt[5]{1511}\) using the function \(g(x) = 15x\), we need to find the values of \(x\) that make \(g(x)\) approach 1511.

1. Start with \(x = 3\):
\[
g(3) = 15 \cdot 3 = 45
\]

Now, we can choose the next five rational values that are greater than 3. We will increment \(x\) to find the next values.

2. Next, we'll test \(x = 4\):
\[
g(4) = 15 \cdot 4 = 60
\]

3. Next, \(x = 5\):
\[
g(5) = 15 \cdot 5 = 75
\]

4. Next, \(x = 6\):
\[
g(6) = 15 \cdot 6 = 90
\]

5. Next, \(x = 7\):
\[
g(7) = 15 \cdot 7 = 105
\]

6. Finally, \(x = 8\):
\[
g(8) = 15 \cdot 8 = 120
\]

Thus, the next five x-values after 3 are:

**The answer is:**
3, 4, 5, 6, 7, 8