complete the table shown to the right for the population growth model for a certain country.\n\nk = \n(round…

Explanation:

Step1: Determine the time ( t )

The year 2005 is the initial year (( t = 0 )), and 2021 is ( t=2021 - 2005=16 ) years later. The population growth model is ( P(t)=P_0e^{kt} ), where ( P_0 = 40.5 ) (in millions) and ( P(16)=59.8 ) (in millions). Substitute into the formula: ( 59.8 = 40.5e^{16k} ).

Step2: Solve for ( k )

First, divide both sides by ( 40.5 ): ( \frac{59.8}{40.5}=e^{16k} ). ( \frac{59.8}{40.5}\approx1.476543 ), so ( 1.476543=e^{16k} ). Take the natural logarithm of both sides: ( \ln(1.476543)=\ln(e^{16k}) ). Since ( \ln(e^{x}) = x ), we have ( \ln(1.476543)=16k ). ( \ln(1.476543)\approx0.3892 ). Then ( k=\frac{\ln(1.476543)}{16} ). ( k=\frac{0.3892}{16}\approx0.0243 ).

Answer:

( 0.0243 )