Question

question
an island population of 20,000, grows by 5% each year, compounded continuously. how many inhabitants will the island have in 5 years according to the exponential growth function?
round your answer down to the nearest integer, and do not include the units in your answer.
sorry, thats incorrect. try again?
25681

Explanation:

Step1: Identify the formula

The formula for continuous - growth is \(P(t)=P_0e^{rt}\), where \(P_0\) is the initial population, \(r\) is the growth rate, and \(t\) is the time.

Step2: Substitute the values

Given \(P_0 = 20000\), \(r=0.05\), and \(t = 5\). Substitute into the formula: \(P(5)=20000e^{(0.05\times5)}\).

Step3: Calculate the exponent

First, calculate \(0.05\times5 = 0.25\). Then, \(P(5)=20000e^{0.25}\).

Step4: Evaluate \(e^{0.25}\)

Using a calculator, \(e^{0.25}\approx1.2840254\).

Step5: Calculate \(P(5)\)

\(P(5)=20000\times1.2840254 = 25680.508\).

Answer:

25680