Exponentially 6065

The intensity of daylight penetrating seawater decreases exponentially depending on its depth. At a depth of 6m, it is reduced by half. The underwater camera needs at least 75% of the daylight intensity for recording. To what depth can we use it under this assumption?

Correct answer:

x =  2.4902 m

Step-by-step explanation:

$$\begin{gathered} (0.5{)}^{x/6}=75/100 \\ x/6\cdot \ln 0.5=\ln 0.75 \\ x=6\cdot \ln 0.75/\ln (0.5)=2.4902\text{m} \end{gathered}$$

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