The exponential function representing exponential decay is given by:
[tex]N(t)=N_0(1+r)^{-t}[/tex]
Given that there were approximately 2.23 million marriages in 2005, compared to 2.28 million in 2004, thus
[tex]2.23=2.28(1+r)^{-1} \\ \\ \Rightarrow(1+r)^{-1}= \frac{2.23}{2.28} =0.9781 \\ \\ \Rightarrow1+r=0.9781^{-1}=1.022 \\ \\ \Rightarrow r=1.022-1=0.022 \ or \ 2.2\%[/tex]
Therefore, the number of marriages in 2025 can be predicted to be:
[tex]N(2025-2004)=2.28(1+0.022)^{-(2025-2004)} \\ \\ N(21)=2.28(1.022)^{-21}=2.28(0.6332)=1.44[/tex]
