MATH7021: Week 12

May 7, 2015 in MATH7021

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Assignments 2

I hope to have the corrections finished tomorrow. If not it will be Monday but no later.

Week 12

We finished the last chapter on Multiple Integration including triple integrals.

Week 13

We will first go over the sample and then have tutorial time.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

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May 16, 2015 at 1:04 pm

Student

Hi J.P.,

Is there any chance you have a solution to Q 3 (c) on the sample paper we have? I’m ending up with $e^{-10t} = 0.2$ but I think I’ve gone wrong somewhere.

Thanks.

May 16, 2015 at 1:10 pm

J.P. McCarthy

We have found in part (i) that

$\theta(t)=50+250e^{-10t}$ .

Now part (ii) asks us when is the temperature equal to 100.

So we are solving

$\theta(t)=100$

$\Rightarrow 50+250e^{-10t}=100$

$\Rightarrow 250e^{-10t}=50$

$\Rightarrow e^{-10t}=\frac{1}{5}$ .

Now you have

$\displaystyle (\text{base})^{\text{power}}=\text{number}$

and using the definition of logarithms we have

$\displaystyle \log_{\text{base}}(\text{number})=\text{power}$

$e^{-10t}=\frac{1}{5}\Rightarrow -10t=\log_e(1/5)=\ln(1/5)$

$\displaystyle \Rightarrow t=\frac{ln\left(\frac15\right)}{-10}\approx 0.161$ s… it cooled fairly quickly there in fairness!

Alternatively note that $e^x$ and $\ln x$ are inverse functions so if we apply $\ln x$ to both sides of $e^{-10t}=\frac{1}{5}$ we have

$\ln\left(e^{-10t}\right)=\ln(1/5)\Rightarrow -10t=\ln(1/5)$ and continue on.

Regards,
J.P.

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MATH7021: Week 12

Assignments 2

Week 12

Week 13

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MATH7021: Week 12

Assignments 2

Week 12

Week 13

Student Resources

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J.P. McCarthy Maths

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