use the formula ( t=\frac{ln 2}{k} ) that gives the time for a population, with a growth rate ( k ), to…

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.\nthe growth model ( a = 9 e^{0.0021 t} ) describes the population, ( a ), of a country in millions, ( t ) years after 2003.\na. what is the countrys growth rate?

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.\nthe growth model ( a = 9 e^{0.0021 t} ) describes the population, ( a ), of a country in millions, ( t ) years after 2003.\na. what is the countrys growth rate?

Answer

Explanation:

Step1: Identify the growth model formula

The general population growth model is (A = A_0e^{kt}). In the given model (A = 9e^{0.0021t}), by comparing with the general formula (A = A_0e^{kt}), we can identify the value of (k).

Step2: Determine the growth rate

In the formula (A = A_0e^{kt}), (k) represents the growth rate. For the model (A = 9e^{0.0021t}), when we compare it with (A = A_0e^{kt}), we have (k = 0.0021). To express it as a percentage, we multiply (k) by (100). So the growth rate as a percentage is (0.0021\times100)%.

Answer:

The country's growth rate is (0.21)%