3. A family of raccoons has settled in a zoo. The number of raccoons $N$ after $t$ years $(t \geq 0)$ is given by the function $N=10 \cdot e^{\frac{2}{5} t}$.

(a) How many raccoons are in the family at the time of settlement?

(b) How many years would it take for the family of raccoons to number 100 members? Round the result to the nearest whole number.

Write down the answers.
3. (a) $t=0$ 0.5 points
$N=10 \cdot e^{\frac{2}{5} \cdot 0}=10$ ..... 1 point
Answer ..... 0.5 points
(b) $N=100 \Rightarrow 100=10 \cdot e^{\frac{2}{5} t}$ ..... 0.5 points
$10=e^{\frac{2}{5} t}$ ..... 0.5 points
$\ln 10=\ln e^{\frac{2}{5} t}$ ..... 0.5 points
$\ln 10=\frac{2}{5} t \ln e$ ..... 0.5 points
$\ln 10=\frac{2}{5} t$ ..... 0.5 points
$t=\frac{5}{2} \ln 10=5.75646 \doteq 5.76$ ..... 1 point
Answer: 6 years ..... 0.5 points