# Chapter 5 - 5.5 - Exponential and Logarithmic Models - 5.5 Exercises - Page 406: 36a

$N= 30 (1-e^{\frac{t}{20} \ln \frac{11}{30}})$

#### Work Step by Step

We need to write the equation for a learning curve. $N= 30 (1-e^{kt})$ Set $(t,N)= (20,19)$ to compute $a$ $19= 30 (1-e^{20k})$ or, $e^{20k}= \dfrac{11}{30}$ Take the $\log$ on each side. $\ln e^{20 k} =\ln \dfrac{11}{30}$ Simplify: $k=\dfrac{1}{20} \ln \dfrac{11}{30}$ So, we have $N= 30 (1-e^{\frac{t}{20} \ln \frac{11}{30}})$

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