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 = 9e^{0.004t} ) describes the population, ( a ), of a country in millions, ( t ) years after 2003.
...
a. what is the country’s growth rate?
%

Explanation:

Step1: Recall the exponential growth model

The general exponential growth model is \( A = A_0 e^{kt} \), where \( A_0 \) is the initial amount, \( k \) is the growth rate, and \( t \) is time. The given model is \( A = 9e^{0.004t} \).

Step2: Identify the growth rate from the model

In the exponential growth formula \( A = A_0 e^{kt} \), the coefficient of \( t \) in the exponent is the growth rate \( k \). Comparing with \( A = 9e^{0.004t} \), we can see that \( k = 0.004 \). To express this as a percentage, we multiply by 100. So the growth rate as a percentage is \( 0.004\times100 = 0.4\% \).

Answer:

The country's growth rate is \( 0.4\% \) (or in decimal form \( 0.004 \)).