## Calculus: Early Transcendentals 8th Edition

The brain was growing at a rate of $~~1.05\times 10^{-8}~g/year$
$W = 0.12~L^{2.53}$ We can find an expression for $B$: $B = 0.007~W^{2/3}$ $B = 0.007~(0.12~L^{2.53})^{2/3}$ $B = 0.001703~L^{1.687}$ We can find $\frac{dL}{dt}$: $\frac{dL}{dt} = \frac{20~cm-15~cm}{10\times 10^6~years}$ $\frac{dL}{dt} = 0.5 \times 10^{-6}~cm/year$ We can find $\frac{dB}{dt}$: $B = 0.001703~L^{1.687}$ $\frac{dB}{dt} = (0.001703)~(1.687~L^{0.687})(\frac{dL}{dt})$ $\frac{dB}{dt} = (0.001703)~(1.687)~(18)^{0.687}(0.5 \times 10^{-6}~cm/year)$ $\frac{dB}{dt} = 0.0105\times 10^{-6}~g/year$ $\frac{dB}{dt} = 1.05\times 10^{-8}~g/year$ The brain was growing at a rate of $~~1.05\times 10^{-8}~g/year$