MS 101 Alg & Trig test two • 11 June 2015 • Name:

1. Calculate or solve for x the following expressions and equations.
   1. ____________ 14⁰
   2. ____________ ${log}_{14}\left(14\right)$
   3. ____________ log 10000
   4. ____________ e^x = 8103.09
   5. ____________ ln x = 2.7726
   6. ____________ ${log}_5\left(\mathrm{x}\right)=2$
   7. ____________ 6 ln(6x) = 32.2517
   8. ____________ $e^{\left(\frac{x}{7}\right)}=1096.6332$
   9. ____________ ln(2) + ln (32) = ln(x)
   10. ____________ 2 log(3) − log(x + 144)= −2 log(5)
   11. ____________ ${\mathrm{x}}^{{\log }_{\mathrm{x}}\mathrm{x}}=100$
   12. ____________ ${log}_{18}\left(12012.562\right)$
2. "A learning curve is a graphical representation of the increase of learning (vertical axis) with experience (horizontal axis). The curve for a single subject may be erratic." - Learning curve. (2013, June 11). In Wikipedia, The Free Encyclopedia. Retrieved 09:59, June 11, 2013 On her very first attempt to ride the RipStik, Keeyana manage to roll a distance of 1.2 meters from one wall to another. On her second attempt she managed to more than double that distance to 5.9 meters. The attempts to ride are experience, the distance she successfully rolled is the learning.
   

   Experience: Attempt number	Learning: Rolling distance (meters)
   1	1.2
   2	5.9
   3	7.2
   4	9.3
   5	9.8
   6	11.3
   7	10.9
   8	12.0
   9	12.1
   10	14.2

   1. Graph the data, add a LOGARITHMIC trend line and equation to the graph, and then write the logarithmic equation:
   2. ____________ Based on the logarithmic equation in part a, calculate the rolling distance for attempt number 15.
   3. ____________ Based on the logarithmic equation in part a, calculate the attempt number when Keeyana will attain a rolling distance of 16 meters.
   4. Solve the equation in part a for x, writing out the resulting inverse equation below:
3. The following chart displays three functions. Each function is shown using a marker of a different shape: circles, squares, and triangles.
   
   1. __________ What marker shape is the exponential growth function $y=\frac{e^x}{1.3}$?
   2. __________ What marker shape is the Gaussian function $y=\frac{9}{e^{0.5x^2}}$?
   3. __________ What marker shape is the logistic function $y=\frac{9}{(1+e^{-3x})}$?
4. Which is your favorite function: exponential growth, exponential decay, logarithmic, Gaussian, or logistic, and why?