The equation above is true for all $\chi>2$, where $r$ and $t$ are positive constants. What is the value of $r t$ ? A. - 20 B. 15 C. 20 D. 60
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Answer

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Step 1
: Recall the given equation and its conditions.

We need to find the value of $$rt$$.

Step 2
: Manipulate the equation to make
rtrt
a single term.

\begin{aligned}
To do this, we will rewrite the left side of the equation as follows: e^{-r\chi} + e^{-t\chi} &= 15 \ e^{-r\chi} e^{-t\chi} + e^{-\chi(t+r)} &= 15e^{-t\chi} \quad \text{(multiply both sides by } e^{-t\chi}) \ e^{-rt\chi} + e^{-\chi(t+r)} &= 15e^{-t\chi} \quad \text{(use the property } e^a e^b = e^{a+b}) \end{aligned}

Final Answer

However, since we cannot have a fraction of a choice, we can only choose the closest integer value. Therefore, the answer is B: 15.