The number of bacteria \( P(t) \) in a certain population increases according to the following function, where time \( t \) is measured in hours. \[ P(t)=3000 e^{0.08 t} \] Find the initial number of bacteria in the population and the number of bacteria after 7 hours. Round your answers to the nearest whole number as necessary. Initial number: bacteria Number after 7 hours: bacteria

Решите неравенство: \( \left(2^{\frac{x-3}{2}}-1\right) \sqrt{2^{x}-6 \sqrt{2^{x}}+8} \geqslant 0 \)

5. \( y=x^{2}+3 x-10 \) and the \( x \)-axis.

Es sei \( \rho(x) \) eine Wahrscheinlichkeitsdichtefunktion (WD), die im Intervall \( [0 ; 2] \) gegeben ist durch \( \rho(x)=N_{0}(1 /(x+1)-1 / 3) \) und Null auBerhalb des Intervalls, \[ \rho(x)=\left\{\begin{array}{ll}N_{0}\left(\frac{1}{x+1}-\frac{1}{3}\right) & \text { fulr } x \in[0,2], \\ 0 & \text { sonst. }\end{array}\right. \] Bestimmen Sie die Konstante \( N_{0} \), so dass \( \rho(x) \) korrekt normiert ist.

Simple interest on ₹ 500 for 4 yr at the rate of \( 8 \% \) per annum is \( \begin{array}{ll}\text { (A) } ₹ 10 & \text { (B) } ₹ 32 \\ \text { (C) } ₹ 40 & \text { (D) } ₹ 160\end{array} \)

\( \frac { 10 x ^ { 2 } - 4 x + 9 } { x } ( x \neq 0 ) \)