Question

MULTIPLE BIRTHS The number of quadruplet births Q in the United States in recent years can be modelled by $\mathit{Q}\mathbf{=}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{5}{\mathit{t}}^3\mathbf{+}\mathbf{11}\mathbf{.}\mathbf{7}{\mathit{t}}^2\mathbf{-}\mathbf{21}\mathbf{.}\mathbf{5}\mathit{t}\mathbf{+}\mathbf{218}\mathbf{.}\mathbf{6}$, where t represents the number of years since 1992. For what values of t does this model no longer allow for realistic predictions? Explain your reasoning?

Short answer

For$t=\mathbf{2025}$ this model will no longer allow realistic predictions.

Step-by-step solution

Step 1. Plot a graph.

Plot the graph of the given equation.

Step 2. Realistic prediction.

When the quadruplet births become 0, it will be difficult to make realistic predictions, as there are no longer births.

Step 3. Write the conclusion.

From the graph it can be observed that the graph starts taking negative Q-values after $Q=0$. Therefore, the prediction can be made when$Q=0$ and after that it will be difficult for this model to make realistic predictions. When graph cuts the x-axis, the point on the graph is $\left(22.351,0\right)$. After$t=22$ years, since 2002 the model no longer allows realistic predictions. Therefore, after the year 2024, that is, from the year 2025 this model no longer allows the realistic predictions.