Question

In the United States, there were approximately 2.23 million marriages in 2005, compared to 2.28 million in 2004. Use an exponential function to predict the number of marriages in 2025, and discuss the reasonableness of the result.

Answer 1

The exponential function representing exponential decay is given by:

$N(t)=N_0(1+r)^{-t}$

Given that there were approximately 2.23 million marriages in 2005, compared to 2.28 million in 2004, thus

$2.23=2.28(1+r)^{-1} \\ \\ \Rightarrow(1+r)^{-1}= \frac{2.23}{2.28} =0.9781 \\ \\ \Rightarrow1+r=0.9781^{-1}=1.022 \\ \\ \Rightarrow r=1.022-1=0.022 \ or \ 2.2\%$

Therefore, the number of marriages in 2025 can be predicted to be:

$N(2025-2004)=2.28(1+0.022)^{-(2025-2004)} \\ \\ N(21)=2.28(1.022)^{-21}=2.28(0.6332)=1.44$