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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