Solutions: Exponential and Logarithmic Functions Practice Test

3. \$1,947

5. y-intercept: (0, 5)

7. ${8.5}^{a}=614.125$

9. $x={\left(\frac{1}{7}\right)}^{2}=\frac{1}{49}$

11. $\mathrm{ln}\left(0.716\right)\approx -0.334$

13. Domain: < 3; Vertical asymptote: = 3; End behavior: $x\to {3}^{-},f\left(x\right)\to -\infty$ and $x\to -\infty ,f\left(x\right)\to \infty$

15. ${\mathrm{log}}_{t}\left(12\right)$

17. $3\mathrm{ln}\left(y\right)+2\mathrm{ln}\left(z\right)+\frac{\mathrm{ln}\left(x - 4\right)}{3}$

19. $x=\frac{\frac{\mathrm{ln}\left(1000\right)}{\mathrm{ln}\left(16\right)}+5}{3}\approx 2.497$

21. $a=\frac{\mathrm{ln}\left(4\right)+8}{10}$

23. no solution

25. $x=\mathrm{ln}\left(9\right)$

27. $x=\pm \frac{3\sqrt{3}}{2}$

29. $f\left(t\right)=112{e}^{-.019792t}$; half-life: about 35 days

31. $T\left(t\right)=36{e}^{-0.025131t}+35;T\left(60\right)\approx {43}^{\text{o}}\text{F}$

33. logarithmic

35. exponential; $y=15.10062{\left(1.24621\right)}^{x}$

37. logistic; $y=\frac{18.41659}{1+7.54644{e}^{-0.68375x}}$