Question 7: The theory of the population and housing census in Rwanda dates back to the 1970's. To date 4 modern censuses having successively been conducted, in \( 1978,1991,2002 \) and 2012 . Based on the population census, in 1978 the total population was 4831527 , in 2002 we had 8128533 and in 2012 the record showed 10515973 of people. Let \( t=0,24,34 \) corresponding to the years 1978,2002 and 2012 respectively. Determine \( K \) as carrying capacity for Rwanda since the population growth rate is approximately \( 3 \%(r=0.03) \).

13. Explain what is wrong with this solution. \( 1+2+4+8+\ldots \) is an infinite geometric series with \( a=1 \) and \( r=2 \). \( \therefore S_{\infty}=\frac{1}{1-2}=-1 \) \( \therefore 1+2+4+8+\ldots=-1 \) So by adding infinitely many positive numbers we get a negative answer

6. (i) Show that the point \( (1,7) \) does not lie on the line \( y=5 x-2 \). (ii) The point \( P \) lies on the line \( y=5 x-2 \). Write down a possible pair of coordinates for \( P \).

questions. If \( n^{3}=x \) and \( n^{4}=20 x \), where \( n>0 \), what is the value of \( x \) ?

195. Розв'язати нерівність: 1) \( 7^{x}<\frac{1}{49} \)

\( \left. \begin{array} { c } { 72 x ^ { 2 } + 160 x \quad t ^ { \prime } ( x ) = 4 x ^ { 2 } \cdot 0 + \ln 3 \cdot 8 x = 8 x : \ln 5 } \\ { \frac { ( 4 x ^ { 2 } \cdot \ln 5 ) ( 72 x ^ { 2 } + 160 x ) - ( 24 x ^ { 3 } + 80 x ^ { 2 } ) \cdot ( 8 x \cdot \ln 5 ) } { [ 4 x ^ { 2 } \cdot \ln 5 ] ^ { 2 } } } \end{array} \right. \)