Solutions: Exponential and Logarithmic Functions Practice Test

1. About 13 dolphins. 3. $1,947 5. y-intercept: (0, 5) 7. [latex]{8.5}^{a}=614.125\\[/latex] 9. [latex]x={\left(\frac{1}{7}\right)}^{2}=\frac{1}{49}\\[/latex] 11. [latex]\mathrm{ln}\left(0.716\right)\approx -0.334\\[/latex] 13. Domain: x < 3; Vertical asymptote: x = 3; End behavior: [latex]x\to {3}^{-},f\left(x\right)\to -\infty \\[/latex] and [latex]x\to -\infty ,f\left(x\right)\to \infty \\[/latex] 15. [latex]{\mathrm{log}}_{t}\left(12\right)\\[/latex] 17. [latex]3\mathrm{ln}\left(y\right)+2\mathrm{ln}\left(z\right)+\frac{\mathrm{ln}\left(x - 4\right)}{3}\\[/latex] 19. [latex]x=\frac{\frac{\mathrm{ln}\left(1000\right)}{\mathrm{ln}\left(16\right)}+5}{3}\approx 2.497\\[/latex] 21. [latex]a=\frac{\mathrm{ln}\left(4\right)+8}{10}\\[/latex] 23. no solution 25. [latex]x=\mathrm{ln}\left(9\right)\\[/latex] 27. [latex]x=\pm \frac{3\sqrt{3}}{2}\\[/latex] 29. [latex]f\left(t\right)=112{e}^{-.019792t}\\[/latex]; half-life: about 35 days 31. [latex]T\left(t\right)=36{e}^{-0.025131t}+35;T\left(60\right)\approx {43}^{\text{o}}\text{F}\\[/latex] 33. logarithmic 35. exponential; [latex]y=15.10062{\left(1.24621\right)}^{x}\\[/latex] 37. logistic; [latex]y=\frac{18.41659}{1+7.54644{e}^{-0.68375x}}\\[/latex]

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