Use an over/under table to estimate the solution to the exponential equation 3+23x=9
to two decimal places.(1 point)
The solution to the exponential equation is x≈
To estimate the solution to the exponential equation 3 + 2^(3x) = 9 using an over/under table, we can start by rearranging the equation to isolate the exponential term:
2^(3x) = 9 - 3
2^(3x) = 6
Now let's create an over/under table by using a few values for x and comparing the value of the exponential term (2^(3x)) to 6:
x | 3x | 2^(3x) | Difference from 6
-----------------------------------------
0 | 0 | 1 | -5
0.5 | 1.5 | 2.83 | -3.17
1 | 3 | 8 | 2
1.5 | 4.5 | 22.63 | 16.63
2 | 6 | 64 | 58
2.5 | 7.5 | 181.02 | 175.02
We can see that as x increases, the value of 2^(3x) also increases. When x is approximately 1, the value of 2^(3x) is close to 6.
Therefore, the solution to the exponential equation 3 + 2^(3x) = 9 is approximately x ≈ 1.