5050 f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Ove

Question

5050

f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Over x EndFractionf(x)=5x+39x

f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Over x EndFractionf(x)=5x+39x

After how many days do the students remember

88

words?The students remember

88

words after

nothing

days.

In an experiment, students are asked to memorize

5050

words. The students are tested each day to see how many words they remember and the class average is then found. The function

f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Over x EndFractionf(x)=5x+39x

models the average number of words remembered by the students, f(x), after x days. The graph of the rational function is shown to the right. 0153001020304050Number of DaysWords Remembered

f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Over x EndFractionf(x)=5x+39x

A coordinate system has a horizontal axis labeled Number of Days from 0 to 30 in increments of 5 and a vertical axis labeled Words Remembered from 0 to 50 in increments of 5. From left to right, a curve labeled f left parenthesis x right parenthesis equals StartFraction 5 x plus 39 Over x EndFraction falls at a decreasing rate from a plotted point at (1, 44) passing through the point (5, 12.8), and then falls shallowly. A horizontal dashed line crosses the vertical axis at 5. All coordinates are approximate.

Explanation / Answer

f(x) = ( 5x + 39 ) / x

plugging f(x) = 8

8 = ( 5x + 39) /x

multiplying both sides by x

8x = 5x + 39

8x - 5x = 39

3x = 39  

x = 13

so after 13 days student remembers 8 words

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