Mathematics, 01.07.2019 17:00 vjacksongonzalez
Differentiate ! the height of a certain species 't' years after it was planted is given by h=20ln(3t +2) +30cm a) how tall was the shrub when it was planted b) how long will it take for the shrub to reach a height of 1 metre c)at what rate is the shrubs height changing i) 3 years after being planted ii) 10 years after being planted
Answers: 2
![\bf h=20ln(3t+2)+30\\\\ -------------------------------\\\\ \boxed{a}\\\\ \stackrel{0~years}{t=0}\qquad h=20ln[3(0)+2]+30\implies h=20ln(2)+30 \\\\\\ h\approx 43.86 \\\\\\ \boxed{b}\\\\ \stackrel{1~meter}{h=100}\qquad 100=20ln(3t+2)+30\implies 70=20ln(3t+2) \\\\\\ \cfrac{70}{20}=ln(3t+2)\implies \stackrel{\textit{log cancellation rule}}{e^{\frac{7}{2}}=e^{ln(3t+2)}}\implies e^{\frac{7}{2}}=3t+2 \\\\\\ e^{\frac{7}{2}}-2=3t\implies \cfrac{e^{\frac{7}{2}}-2}{3}=t\implies 10.371817\approx t](/tpl/images/0039/3830/b9d25.png)
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