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Solutions: Exponential and Logarithmic Functions Practice Test

1. About 13 dolphins. 3. $1,947 5. y-intercept: (0, 5) Graph of f(-x)=5(0.5)^-x in blue and f(x)=5(0.5)^x in orange. 7. 8.5a=614.125{8.5}^{a}=614.125 9. x=(17)2=149x={\left(\frac{1}{7}\right)}^{2}=\frac{1}{49} 11. ln(0.716)0.334\mathrm{ln}\left(0.716\right)\approx -0.334 13. Domain: < 3; Vertical asymptote: = 3; End behavior: x3,f(x)x\to {3}^{-},f\left(x\right)\to -\infty and x,f(x)x\to -\infty ,f\left(x\right)\to \infty 15. logt(12){\mathrm{log}}_{t}\left(12\right) 17. 3ln(y)+2ln(z)+ln(x4)33\mathrm{ln}\left(y\right)+2\mathrm{ln}\left(z\right)+\frac{\mathrm{ln}\left(x - 4\right)}{3} 19. x=ln(1000)ln(16)+532.497x=\frac{\frac{\mathrm{ln}\left(1000\right)}{\mathrm{ln}\left(16\right)}+5}{3}\approx 2.497 21. a=ln(4)+810a=\frac{\mathrm{ln}\left(4\right)+8}{10} 23. no solution 25. x=ln(9)x=\mathrm{ln}\left(9\right) 27. x=±332x=\pm \frac{3\sqrt{3}}{2} 29. f(t)=112e.019792tf\left(t\right)=112{e}^{-.019792t}; half-life: about 35 days 31. T(t)=36e0.025131t+35;T(60)43oFT\left(t\right)=36{e}^{-0.025131t}+35;T\left(60\right)\approx {43}^{\text{o}}\text{F} 33. logarithmic Graph of the table’s values. 35. exponential; y=15.10062(1.24621)xy=15.10062{\left(1.24621\right)}^{x} Graph of the table’s values. 37. logistic; y=18.416591+7.54644e0.68375xy=\frac{18.41659}{1+7.54644{e}^{-0.68375x}} Graph of the table’s values.

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  • Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..