Science:Math Exam Resources/Courses/MATH102/December 2014/Question A 06

MATH102 December 2014

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Question A 06
The figure below shows $\ln(C(t))$ plotted against $t$ as the best-fit line through the data points. Which of the following expressions for $C(t)$ corresponds to that best-fit line? LogPlot $C(t)={\frac {1}{2}}+{\frac {3}{4}}t$ $C(t)={\frac {3}{4}}+{\frac {1}{2}}t$ $C(t)={\frac {1}{2}}e^{{\frac {3}{4}}t}$ $C(t)=e^{\frac {1}{2}}e^{{\frac {3}{4}}t}$ $C(t)=e^{\frac {3}{4}}e^{{\frac {1}{2}}t}$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
What do the slope and intercept in a log plot represent?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. From the graph we observe the y-intercept of the line is ${\frac {1}{2}}$ and suppose the slope of the line is k. Then we can write down the equation of the line $y={\frac {1}{2}}+kt,$ But notice the y-axis is $\ln(C(t))$, then we have ${\begin{aligned}\ln(C(t))&={\frac {1}{2}}+kt,\\C(t)&=e^{{\frac {1}{2}}+kt},\\{\text{or }}C(t)&=e^{\frac {1}{2}}e^{kt},\end{aligned}}$ where the only possible answer is (d).