QuestionA child is 20 inches at birth. Find the percent of adult height at age 15 using $f(x)=20+47 \log (x+2)$ .

Studdy Solution

STEP 1

Assumptions1. The child is20 inches long at birth. . The growth of the child is modeled by the logarithmic function $f(x)=20+47 \log (x+)$ 3. $x$ represents the child's age in years.
4. $f(x)$ represents the percentage of the child's adult height reached at age $x$ .

STEP 2

To find the percentage of the child's adult height attained by age15, we need to substitute $x$ with15 in the given function.
$f(15) =20 +47 \log (15+2)$

STEP 3

implify the argument of the logarithm.
$f(15) =20 +47 \log (17)$

STEP 4

Calculate the value of the logarithm and multiply it by47.
$f(15) =20 +47 \times \log (17)$

STEP 5

Add20 to the result from the previous step to find the percentage of the child's adult height attained by age15.
$f(15) =20 +47 \times \log (17)$

STEP 6

Calculate the value of $f(15)$ .
$f(15) =20 +47 \times \log (17) =20 +47 \times1.23 =77.81$

STEP 7

Round the result to the nearest whole percentage.
$f(15) =78\%$ The child has attained78% of her adult height by age15.

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