Chapter 4 - Exponential Functions - 4.2 Comparing Exponential and Linear Functions - Exercises and Problems for Section 4.2 - Exercises and Problems - Page 154: 10

$ g(t)=70.711\cdot (0.966)^t $

We are given that $g(10)= 50$ and $g(30)= 25$. The ratio method gives: $$ \begin{aligned} \frac{a b^{30}}{a b^{10}} & =\frac{g(30)}{g(10)} \\ b^{20} & =\frac{25}{50} \\ b & =\left(\frac{25}{50}\right)^{1 / 20} \approx 0.966 \end{aligned} $$ $$ \begin{aligned} a(0.965936)^{10} & =50 \\ a & =\frac{50}{(0.965936)^{10}} \approx 70.711 \end{aligned} $$ It follows that $$ g(t)=70.711\cdot (0.966)^t $$