Chapter 5 - 5.5 - Exponential and Logarithmic Models - 5.5 Exercises - Page 405: 25

$y= e^{\frac{x}{3}\ln 10}$

We have $y=ae^{bx}$ Set $(x,y)= (0,1)$ So, $1=ae^{b(0)} \implies a=1$ Further, we have $y=ae^{bx}$ Set $(x,y)= (3,10)$ to compute $b$ So, $10=ae^{3b} \implies e^{3b}=10$ and $\ln 10 =\ln e^{3b} \implies b =\dfrac{1}{3} \ln 10$ Now, the exponential decay model is: $y= e^{\frac{x}{3}\ln 10}$