Science:Math Exam Resources/Courses/MATH103/April 2009/Question 08 (c)

MATH103 April 2009

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Question 08 (c)
The growth rate of a plant during the first week after germination is given by $\displaystyle g(t)=ae^{t/2}{\text{ mm/day}},$ where the time t is measured in days, and a is a constant. How much did the plant grow on the fifth day (i.e. between t = 4 and t = 5)? (If you don't know the constant a, use a = 1.)

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
How can you use the height function $h(t)\$ to know the change of the height between day $\ 4$ and day $\ 5$.

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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. The change of height between day $\ 4$ and $\ 5$ is ${\begin{aligned}\ h(5)-h(4)&={\frac {e^{\frac {5}{2}}-1}{e^{\frac {1}{2}}-1}}-{\frac {e^{\frac {4}{2}}-1}{e^{\frac {1}{2}}-1}}\\&={\frac {e^{2.5}-e^{2}}{e^{\frac {1}{2}}-1}}=e^{2}{\frac {e^{\frac {1}{2}}-1}{e^{\frac {1}{2}}-1}}=e^{2}\end{aligned}}$

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