The age T, in years, of a haddock can be thought of as a function of its length L, in centimeters. One common model uses the natural logarithm, as shown in the following equation.
T = 19 − 5 ln(53 − L)
How long is a haddock that is 12 years old? (Round your answer to two decimal places.)
+26400 The age T, in years, of a haddock can be thought of as a function of its length L, in centimeters. One common model uses the natural logarithm, as shown in the following equation.
T = 19 − 5 ln(53 − L)
How long is a haddock that is 12 years old? (Round your answer to two decimal places.)
\(\begin{array}{rcl} T &=& 19 - 5 \cdot\ln{(53 - L)} \qquad & | \qquad +5 \cdot\ln{(53 - L)}\\ T+5 \cdot\ln{(53 - L)} &=& 19 \qquad & | \qquad -T\\ 5 \cdot \ln{(53 - L)} &=& 19-T \qquad & | \qquad :5\\ \ln{(53 - L)} &=& \frac{ 19-T }{5} \qquad & | \qquad e^{()}\\ 53 - L &=& e^{\frac{ 19-T }{5}} \qquad & | \qquad \cdot(-1)\\ -53 + L &=& -e^{\frac{ 19-T }{5}} \qquad & | \qquad +53\\ L &=& -e^{\frac{ 19-T }{5}} +53\\ \boxed{~ \begin{array}{lcl} L &=& 53-e^{\frac{ 19-T }{5}} \end{array} ~}\\\\ T&=&12 \text{ years old} \\ L &=& 53-e^{\frac{ 19-12 }{5}} \\ L &=& 53-e^{\frac{ 7 }{5}} \\ L &=& 53-e^{1.4} \\ L &=& 53-4.0551999668 \\ L &=& 48.9448000332 \end{array}\)
A 12 years old haddock is 48.94 cm long.
