Chapter 4 - Exponential Functions - 4.2 Comparing Exponential and Linear Functions - Exercises and Problems for Section 4.2 - Exercises and Problems - Page 156: 39

$ N=191+1.9t $ $ N=191(1.0095)^t $

Take $t= 0$ for 2010 so that $t= 10$ corresponds to the 2010. Let $N= b+mt$, then $N= 191+m\cdot0 = 191=b$. We find the slope from: $$ m=\frac{\Delta N}{\Delta t}=\frac{210-191}{10-0}=1.9 $$ The required formula is $$ N=191+1.9t $$ Let $N(t)=a(b)^t $ for the exponential of licensed drivers in the US. The value of $a$ can be taken directly from problem as $a= 191$. We now have $N(t)= 191(b)^t$. Use the point (10,210) to find the value of $b$. $$ \begin{aligned} N & =1918 b^t \\ 191 b^{10}& =210 \\ b^{10} & =\frac{210}{191}=1.0995 \\ b & =(1.0995)^{1 / 10}=1.0095 \end{aligned} $$ The required formula is $$ N=191(1.0095)^t $$