# Chapter 6 - Differential Equations - Review Exercises: 23

$y=0.75e^{0.3794t}$

#### Work Step by Step

$(0, \frac{3}{4})$ lies on the curve. Thus, $$\frac{3}{4} = Ce^{k.0}$$ Or, $$C=\frac{3}{4}=0.75$$ $(5, 5)$ lies on the curve. Thus, $$5 = 0.75e^{5k}$$ Or, $$e^{5k}=\frac{20}{3}$$ $$k = \frac{\ln(20/3)}{5} = 0.3794$$ So, the function is $$y=0.75e^{0.3794t}$$

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