The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the number of years after 2013.† Find the instantaneous rate of change of the population in the year 2048.

Answer:[tex]\frac{dP}{dt} \left \{ {{t=2048} =4.498millions[/tex]Step-by-step explanation:In order to find  the instantaneous rate of change of the population in the year 2048 it is necessary to derivate the function P(t), so:[tex]\frac{dP(t)}{dt} =317*0.01*e^{0.01t} =3.17*e^{0.01t}[/tex]Now, let's find the total of years between 2013 and 2048:[tex]2048-2013=35[/tex]Finally, let's evaluate the derivative function at t=35[tex]\frac{dP}{dt} \left \{ {{t=2048} = 3.17*e^{0.01*(35)} =3.17*e^{0.35}=3.17*1.419067549\\[/tex][tex]\frac{dP}{dt} \left \{ {{t=2048} = 4.498444129 \approx4.498millions[/tex]