## All Tasks

#### Logarithm Properties: The product rule

Wich of the following expressions is equal to $\log_b(x \cdot y)$?

# Logarithm properties

Learning

10

#### Calculating with the Derivative of e

Calculate the derivative for $f(x)=3e^x$ and $g(x)=e^{x^2}$ and give the answer for $f'(2)$ and $g'(2)$. Round to three decimal places.

# Derivation of functions

Training

11

#### Velocity of a Stone

The velocity of a stone sinking in a lake is given by \begin{equation}v(t)=2.5\cdot(1-e^{-0.1\cdot t})\end{equation} with $t$ in seconds and $v(t)$ in $\frac{m}{s}$.
How fast is the stone sinking at the beginning? How fast after ten seconds?
Round to three decimal places, if needed.

# Exponential function

Modeling

11

#### Frequencies

In the table above you can see the basketball results of the four children- namely Lena, Angeló, Marie and Juan. Which of them has the best scoring rate and it’s therefore the best player of the game? Tick the right name!

# Equations & Inequations

Training

6

#### Intersection of two linear functions

Determinate the intersection point of the two linear functions:
$f(x)=-1,5x-1\\ g(x)=3x+8$.

# Linear functions

Training

8

#### An equation with functions

Let $f(x)=xe^x$.
Which $x\in\mathbb{R}$ solves the equation
$f'(x)-f(x)=0$?

# Exponential function

Reasoning

10