Question

use the formula ( t=\frac{ln 2}{k} ) that gives the time for a population, with a growth rate ( k ), to double, to answer the following questions. the growth model ( a = 7 e^{0.004 t} ) describes the population, ( a ), of a country in millions, ( t ) years after 2003. a. what is the countrys growth rate? (square %)

Explanation:

Step1: Identify the growth model form

The general exponential growth model is \(A = A_0e^{kt}\), where \(k\) is the growth rate.

Step2: Compare with given model

Given \(A = 7e^{0.004t}\), comparing with \(A = A_0e^{kt}\), we can see that \(k = 0.004\).

Step3: Convert to percentage

To convert \(k\) to a percentage, we multiply by \(100\). So \(0.004\times100 = 0.4\).

Answer:

\(0.4\)