Chapter 4.1, Problem 73E

Population growth. The rates of changes in population for two cities are as followers:

$\text{Alphaville}:P^{\prime }\left(t\right)=45$,

$\text{Betaburgh}:Q^{\prime }\left(t\right)=105e^{0.3t}$,

Where is the number of years since 2000, and both $P\text{'}\left(x\right)$ and $Q\text{'}\left(x\right)$ are measured in people year. In 2000, Alphaville has a population of 5000, and Betaburgh had a population of 3500.

Determine the population models for both cities.

What were the populations of Alphaville and Betaburgh, to the nearest, in 2010?

c. Sketch the graph of each city’s population model, and estimate the year in which the two cities have the same population.