Exercise 2 | Wiskunde op Tilburg University

Consider the production function

$P(t)=e^t\sqrt{t}$ . Determine the rate of production at

$t=4$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$4e^4$

Antwoord 2 correct

Fout

Antwoord 3 optie

$4\frac{1}{2}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$\frac{1}{4}e^4$

Antwoord 4 correct

Fout

Antwoord 1 optie

$2\frac{1}{4}e^4$

Antwoord 1 feedback

Correct: The rate of production is

$\begin{align*} P'(t)& =e^t\sqrt{t}+e^t\frac{1}{2\sqrt{t}}\\ & =e^t(\sqrt{t}+\frac{1}{2\sqrt{t}}). \end{align*}$

Hence, at

$t=4$ this gives

$P'(4)=e^4(\sqrt{4}+\frac{1}{2\sqrt{4}})=2\frac{1}{4}e^4$ .

Go on.

Antwoord 2 feedback

Wrong: The rate of production at

$t=4$ is not

Antwoord 3 feedback

Wrong: The production rate is not equal to the elasticity.

See Rate production process and Elasticity.

Antwoord 4 feedback

Wrong: You have to apply the product rule.

See Rules of differentiation.