Assessment Problems

1. Graph the system: \( y = 2x + 1 \) and \( y = -x + 4 \) and determine the solution.
2. Solve algebraically: \[ \begin{cases} y = x + 5 \\ 2x - y = 1 \end{cases} \]
3. Simplify: \( 3^4 \cdot 3^2 \)
4. Simplify: \( (2^3)^4 \)
5. Evaluate exponential function: \( f(x) = 5 \cdot 2^x \) for \( x = 3 \)
6. Determine if \( g(x) = 100 \cdot 0.7^x \) represents growth or decay
7. Write a system of equations for a scenario where two lines intersect at (4, 5)
8. Determine the number of solutions for the system: \( y = 2x + 3 \), \( y = 2x - 1 \)
9. Graph \( f(x) = 3 \cdot (0.5)^x \) for x = 0,1,2,3
10. Real-life problem: A bacteria culture doubles every 2 hours, initial = 50. Write exponential function and find population after 6 hours.