Exercise 2 | Wiskunde op Tilburg University

Determine the point of intersection of the graphs of the functions

$f(x)=60+4^x$ and

$g(x)=4^{x+2}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

There is no point of intersection.

Antwoord 2 correct

Fout

Antwoord 3 optie

$(2,76)$

Antwoord 3 correct

Fout

Antwoord 4 optie

$(3,124)$

Antwoord 4 correct

Fout

Antwoord 1 optie

The correct answer is not among the other options.

Antwoord 1 feedback

Correct:

$\begin{align*} 60+4^x=4^{x+2} &\Leftrightarrow 60+4^x = 4^2\cdot 4^x\\ &\Leftrightarrow 60+4^x =16\cdot 4^x\\ &\Leftrightarrow 60 =15\cdot 4^x\\ &\Leftrightarrow 4 = 4^x\\ &\Leftrightarrow x = 1. \end{align*}$

$f(1)=64$ . Hence, the point of intersection is

$(1,64)$ .

Go on.

Antwoord 2 feedback

Wrong: There is a point of intersection.

See Properties exponential functions and Feature exponential functions.

Antwoord 3 feedback

Wrong:

$f(2)=76$ , but

$g(2)=256$ .

See Properties exponential functions and Feature exponential functions.

Antwoord 4 feedback

Wrong:

$f(3)=124$ , but

$g(3)=1024$ .

See Properties exponential functions and Feature exponential functions.