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At what depth is there only one percent of surface sunlight? Do not round until the final answer the round to the nearest whole number as needed

At what depth is there only one percent of surface sunlight? Do not round until the-example-1
User Peterhack
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1 Answer

9 votes
9 votes

SOLUTION

From the question, we have been given the function as


\begin{gathered} f(x)=20(0.995)^x \\ where\text{ f\lparen x\rparen represents percent sunlight } \\ x\text{ distance in feet } \end{gathered}

To solve this we substitute 1 for f(x) and solve the equation, we have


\begin{gathered} f(x)=20(0.995)^x \\ 1=20(0.995)^x \\ 0.995^x=(1)/(20) \end{gathered}

Taking log of both sides


\begin{gathered} log(0.995)^x=log((1)/(20)) \\ xlog0.995=log((1)/(20)) \\ x=(log((1)/(20)))/(log0.995) \\ x=597.64733 \end{gathered}

Hence the answer is 598 feet to the nearest whole number

This is shown on the graph as follows

The point (598, 1)

At what depth is there only one percent of surface sunlight? Do not round until the-example-1
User Arma
by
3.3k points