# Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set - Page 485: 20

$t=\frac{rK}{r+K}$

#### Work Step by Step

Multiply $r-t$ to both sides of the equation: $$\require{cancel} (r-t) \cdot K=(r-t)\cdot \frac{rt}{r-t} \\(r-t) \cdot K=\cancel{(r-t)}\cdot \frac{rt}{\cancel{r-t}} \\rK-tK=rt$$ Add $tK$ to both sides: $$rK-tK+tK=rt+tK \\rK=rt+tK$$ Factor out $t$: $$rK=t(r+K)$$ Divide $(r+K)$ to both sides: $\frac{rK}{r+K}=\frac{t(r+K)}{r+K} \\\frac{rK}{r+K}=t$

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