12) The country of Benin in West Africa has a population of \( 9.05 \) million people. The population is growing at a rate of \( 3.1 \% \) each year. Which function can be used to find the population \( 7 \) years from now?
1) \( f ( t ) = ( 9.05 \times 10 ^ { 6 } ) ( 1 - 0.31 ) ^ { 7 } \)
2) \( f ( t ) = ( 9.05 \times 10 ^ { 6 } ) ( 1 + 0.31 ) ^ { 7 } \)
3) \( f ( t ) = ( 9.05 \times 10 ^ { 6 } ) ( 1 + 0.031 ) ^ { 7 } \)
4) \( f ( t ) = ( 9.05 \times 10 ^ { 6 } ) ( 1 - 0.031 ) ^ { 7 }\)
option 3
If \( y = f ( g ( h ( x ) ) ) , \) then the derivative \( y ^ { \prime } \) is given by which for
a) \( f ^ { \prime } ( g ( h ( x ) ) \)
b) \( f ^ { \prime } ( g ( h ( x ) ) h ^ { \prime } ( x ) \)
c) None of these
d) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) \)
e) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) h ^ { \prime } ( x )\)
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
