Answer
a. $82.3$ (million)
b. The population of Germany is decreasing.
c. approximately in the year 2020
Work Step by Step
a. insert t=0 (0 years after 2010) into the formula
$A=82.3e^{-0.004\cdot 0}=82.3$ (million)
b. Exponential models with negative k are decay models.
The population of Germany is decreasing.
c. Insert A=79.1 into the formula and solve for t
$79.1=82.3e^{-0.004\cdot t} \qquad /\div 82.3$
$\displaystyle \frac{79.1}{82.3}=e^{-0.004\cdot t}\qquad$... apply ln( ) to both sides...
$\displaystyle \ln\frac{79.1}{82.3}=-0.004\cdot t\qquad/\div-0.004$
$ t=\displaystyle \frac{\ln\frac{79.1}{82.3}}{-0.004}\approx$9.91455822735$\approx$10 (years after 2010)
The population will be 79,1 million
approximately in the year 2020
