Exponents and Exponential Functions
Unit Test
1. Simplify the following expression: \(2^4 \cdot 2^3\).
2. Express \(4^3\) as a single power of 4.
3. Solve the exponential equation \(3^x = 9\).
4. Evaluate the exponential function \(f(x) = 2^x\) for \(x = 2\) and \(x = 3\).
5. Write the exponential function in the form \(y = a \cdot b^x\) given the exponential function \(f(x) = 5 \cdot 3^x\).
6. Solve the exponential equation \(6^{2x} = 36\).
7. Find the inverse of the exponential function \(g(x) = 4^x\).
8. Graph the exponential function \(h(x) = 2^x\) on the coordinate plane.
9. Evaluate the exponential function \(k(x) = 3^{x-1}\) for \(x = 2\) and \(x = 3\).
10. Write the exponential function in the form \(y = a \cdot b^x\) given the exponential function \(m(x) = 10 \cdot 2^{x-2}\).