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 \( \sqrt[3]{1511} \) using the function \( g(x) = 15x \), we can identify a reasonable starting point and determine the next five values of \( x \) that will lead us toward approximating the cube root.

The cube root of a number \( a \) can be approximated using the function \( g(x) = ax \) to find a value of \( x \) such that \( g(x) \) is approximately equal to the number you want to find the cube root of.

Starting with \( x = 3 \):

1. **Next x-value**: We can make an educated guess for the subsequent values by increasing them slightly. Let's say \( x = 3 + 1 = 4 \).
2. **Next x-values**: Then we'll add 1 again, leading to \( 5, 6, 7, \) and \( 8 \).

Here we go:

- \( 3 \)
- \( 4 \)
- \( 5 \)
- \( 6 \)
- \( 7 \)
- \( 8 \)

So the sequence becomes:

**3, 4, 5, 6, 7, 8**.

In conclusion, starting from 3, the next five \( x \)-values that can be used to approximate \( \sqrt[3]{1511} \) are \( 4, 5, 6, 7, \) and \( 8 \).