Let's start with the linear model given in part (a):

$P(t) = -0.014t + 1.94$

This model represents the population $P(t)$ in millions, where $t$ is the number of years since July 1, 1970.

For part (b), we need to estimate the population of Philadelphia on July 1, 1984.

1. First, determine the value of $t$ corresponding to July 1, 1984. Since $t = 0$ represents July 1, 1970, we have:

$t = 1984 - 1970 = 14$

2. Substitute $t = 14$ into the linear model to find $P(14)$:

$P(14) = -0.014(14) + 1.94$

3. Calculate the value:

$P(14) = -0.196 + 1.94 = 1.744 \text{ million people}$

So, the estimated population of Philadelphia on July 1, 1984, is 1.744 million people.

Would you like more details on this process or any additional explanations?

Here are 5 related questions you might find interesting:

1. How would the population model change if the decline rate were different?
2. What would the population be in 2020 according to this model?
3. How can we check the accuracy of this linear model?
4. What other models could describe population changes over time?
5. How would the model change if there were a population increase instead of a decrease?

Tip: When using linear models, always double-check the slope to ensure it accurately represents the rate of change over time.