Question 10 The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 23700 . (a) Find a function that models the population $t$ years after 2000 ( $t=0$ for 2000). Hint: Use an exponential function with base $e$. Your answer is $P(t)=$
Solution
Step 1 ：The problem is asking for a function that models the population growth of foxes in a certain region. The population growth is continuous and at a rate of 4 percent per year. The initial population in the year 2000 was 23700.
Step 2 ：We can model this using an exponential function with base e. The general form of such a function is \(P(t) = P0 * e^{rt}\), where \(P0\) is the initial population, \(r\) is the growth rate, and \(t\) is the time in years.
Step 3 ：In this case, \(P0 = 23700\), \(r = 0.04\) (4 percent expressed as a decimal), and \(t\) is the number of years after 2000.
Step 4 ：So, the function we're looking for is \(P(t) = 23700 * e^{0.04t}\).
Step 5 ：\(\boxed{P(t) = 23700 * e^{0.04t}}\) is the function that models the population \(t\) years after 2000.
