Select the correct answer.
Consider functions f and g.
\begin{array}{rclC40B40}f\left ( x \right )&=&\frac{1}{4}x^{3}\:+\:2x\:-\:1\\ g\left ( x \right )&=&5^{\left ( x-1 \right )}\:-\:3 \end{array}
Using a table of values, what is an approximate solution to the equation
to the nearest quarter of a unit?
A. x≈1.75
B. x≈2.5
C. x≈1.5
D. x≈2.25
We can create a table of values for both functions f and g to approximate the solution to the equation:
\begin{array}{|c|c|c|} \hline
x & f(x) & g(x) \\ \hline
1 & 1.75 & 1 \\ \hline
1.25 & 1.953125 & 5.5 \\ \hline
1.5 & 2.9375 & 13 \\ \hline
1.75 & 5.5625 & 31 \\ \hline
2 & 9 & 69 \\ \hline
2.25 & 14.0625 & 155 \\ \hline
2.5 & 21.875 & 347 \\ \hline
\end{array}
From the table of values, we can see that the values of f(x) and g(x) are close to each other when x is approximately 2.25. Therefore, an approximate solution to the equation is x≈2.25.
The correct answer is D. x≈2.25.