Let P(t) be the percentage of Americans under the age of 18 at time t. The table gives values of this function in census years from 1950 to 2000. How would it be possible to get more accurate values for P'(t).
get a better table
To obtain more accurate values for P'(t), the derivative of the function P(t), you would need more data points or information about the function P(t) at different time intervals. One way to achieve this is by obtaining data from additional years between the census years provided (1950 to 2000).
Here are a few methods to estimate P'(t) with more accuracy:
1. Interpolation: Using interpolation techniques, you can estimate the values of P(t) between the given census years. This involves creating a smooth curve or line that passes through the known data points and using it to estimate the values of P(t) at any desired time interval.
2. Extrapolation: Assuming that the trend observed in the given census years continues, you can estimate the values of P(t) beyond the provided range. However, it is important to be cautious when extrapolating, as the assumption of a continued trend may not always be valid.
3. Statistical Modeling: By analyzing the available data and using appropriate statistical models or regression analysis, you can estimate the values of P(t) for the years not covered in the dataset. This approach allows for accounting possible variations or trends over time.
4. Surveys or Additional Data Collection: Conducting additional surveys or collecting data from other sources specifically targeted towards the age distribution of the population can provide more accurate values for P(t). These data points can then be used to calculate P'(t) more precisely.
It's also worth mentioning that the accuracy of estimating P'(t) depends on the reliability and representativeness of the data collected, as well as the assumptions made during the estimation process.